M9140 Theoretical Numerical Analysis

Faculty of Science
Autumn 2020
Extent and Intensity
2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 8:00–9:50 M3,01023
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods. Student will be able to understand modern methods of numerical analysis.
Learning outcomes
Student obtains a universal view to numerical mathematics and will be able to apply modern numerical methods in practise
Syllabus
  • Survey of basic concepts and theorems of functional analysis
  • Approximation theory-interpolation theoRy,best approximation theory, best approximation in inner spaces
  • Pseudometric spaces, a general fixed point theorem in pseudometric spaces and its application
  • Convergence factors and their relations
  • Differential calculus for nonlinear operators, Newton's method in a Banach space
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
Teaching methods
Lecture: 2 hours weekly, theoretical preparation
Assessment methods
Lecture. Oral exam.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018.

M9140 Theoretical Numerical Analysis I

Faculty of Science
Autumn 2018
Extent and Intensity
2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 17. 9. to Fri 14. 12. Wed 8:00–9:50 M6,01011
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods. Student will be able to understand modern methods of numerical analysis.
Syllabus
  • Survey of basic concepts and theorems of functional analysis
  • Approximation theory-interpolation theoRy,best approximation theory, best approximation in inner spaces
  • Pseudometric spaces, a general fixed point theorem in pseudometric spaces and its application
  • Convergence factors and their relations
  • Differential calculus for nonlinear operators, Newton's method in a Banach space
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
Teaching methods
Lecture: 2 hours weekly, theoretical preparation
Assessment methods
Lecture. Oral exam.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2020.

M9140 Theoretical Numerical Analysis I

Faculty of Science
Autumn 2016
Extent and Intensity
2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 19. 9. to Sun 18. 12. Tue 8:00–9:50 M3,01023
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods. Student will be able to understand modern methods of numerical analysis.
Syllabus
  • Survey of basic concepts and theorems of functional analysis
  • Approximation theory-interpolation theoRy,best approximation theory, best approximation in inner spaces
  • Pseudometric spaces, a general fixed point theorem in pseudometric spaces and its application
  • Convergence factors and their relations
  • Differential calculus for nonlinear operators, Newton's method in a Banach space
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
Teaching methods
Lecture: 2 hours weekly, theoretical preparation
Assessment methods
Lecture. Oral exam.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2018, Autumn 2020.

M9140 Theoretical Numerical Analysis I

Faculty of Science
Autumn 2014
Extent and Intensity
2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Tue 10:00–11:50 MS1,01016
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods. Student will be able to understand modern methods of numerical analysis.
Syllabus
  • Survey of basic concepts and theorems of functional analysis
  • Approximation theory-interpolation theoRy,best approximation theory, best approximation in inner spaces
  • Pseudometric spaces, a general fixed point theorem in pseudometric spaces and its application
  • Convergence factors and their relations
  • Differential calculus for nonlinear operators, Newton's method in a Banach space
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
Teaching methods
Lecture: 2 hours weekly, theoretical preparation
Assessment methods
Lecture. Oral exam.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2016, Autumn 2018, Autumn 2020.

M9140 Theoretical Numerical Analysis I

Faculty of Science
Autumn 2012
Extent and Intensity
2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Mon 14:00–15:50 MS1,01016
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Applied Mathematics)
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods.
Syllabus
  • Survey of basic concepts and theorems of functional analysis
  • Approximation theory-interpolation theoRy,best approximation theory, best approximation in inner spaces
  • Pseudometric spaces, a general fixed point theorem in pseudometric spaces and its application
  • Convergence factors and their relations
  • Differential calculus for nonlinear operators, Newton's method in a Banach space
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
Teaching methods
Lecture: 2 hours weekly, theoretical preparation
Assessment methods
Lecture. Oral exam.
Language of instruction
Czech
Follow-Up Courses
Further Comments
Study Materials
The course is taught annually.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.

M9140 Theoretical Numerical Analysis I

Faculty of Science
Autumn 2010
Extent and Intensity
2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 8:00–9:50 MS1,01016
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Applied Mathematics)
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods.
Syllabus
  • Survey of basic concepts and theorems of functional analysis
  • Approximation theory-interpolation theoRy,best approximation theory, best approximation in inner spaces
  • Pseudometric spaces, a general fixed point theorem in pseudometric spaces and its application
  • Convergence factors and their relations
  • Differential calculus for nonlinear operators, Newton's method in a Banach space
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
Teaching methods
Lecture: 2 hours weekly, theoretical preparation
Assessment methods
Lecture. Oral exam.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.

M9140 Theoretical Numerical Analysis I

Faculty of Science
Autumn 2009
Extent and Intensity
2/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 8:00–9:50 MS1,01016
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Applied Mathematics)
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods.
Syllabus
  • Survey of basic concepts and theorems of functional analysis
  • Approximation theory-interpolation theoRy,best approximation theory, best approximation in inner spaces
  • Pseudometric spaces, a general fixed point theorem in pseudometric spaces and its application
  • Convergence factors and their relations
  • Differential calculus for nonlinear operators, Newton's method in a Banach space
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
Teaching methods
Lecture: 2 hours weekly, theoretical preparation
Assessment methods
Lecture. Oral exam.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.

M9140 Theoretical Numerical Analysis I

Faculty of Science
Autumn 2008
Extent and Intensity
2/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Wed 8:00–9:50 MS1,01016
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Applied Mathematics)
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods.
Syllabus
  • Survey of basic concepts and theorems of functional analysis
  • Approximation theory-interpolation theoRy,best approximation theory, best approximation in inner spaces
  • Pseudometric spaces, a general fixed point theorem in pseudometric spaces and its application
  • Convergence factors and their relations
  • Differential calculus for nonlinear operators, Newton's method in a Banach space
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
Assessment methods
Lecture. Oral exam.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.

M9140 Theoretical Numerical Analysis I

Faculty of Science
Autumn 2007
Extent and Intensity
2/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Timetable
Thu 10:00–11:50 UP2
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Applied Mathematics)
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. In this course the general theory of iterative processes is built. Further more minimization methods are studied because it is natural to transfer the problem of solving a system to the problem of minimization of a certain functional. Splines are also very important tool of applied mathematics and their general construction can be described in terms of functional analysis. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods.
Syllabus
  • Survey of basic concepts and theorems of functional analysis. Approximation theory-interpolation theoty,best approximation theory. General iterative process and its application. Algorithms of basic iterative methods for solving systems of nonlinear equations. One-step stationary iterative methods. Embeddings methods. Multistep methods. Minimization methods- gradient methods,conjugate gradient method, Gauss-Newton method. Spaces of splines,dimension,defect,B-splines.
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
  • MARČUK, Gurij Ivanovič. Metody numerické matematiky. Vyd. 1. Praha: Academia, 1987, 528 s. URL info
Assessment methods (in Czech)
Přednáška. Zkouška ústní.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.

M9140 Theoretical Numerical Analysis I

Faculty of Science
Autumn 2006
Extent and Intensity
2/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivanka Horová, CSc.
Timetable
Tue 10:00–11:50 07011
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Applied Mathematics)
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. In this course the general theory of iterative processes is built. Further more minimization methods are studied because it is natural to transfer the problem of solving a system to the problem of minimization of a certain functional. Splines are also very important tool of applied mathematics and their general construction can be described in terms of functional analysis. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods.
Syllabus
  • Survey of basic concepts and theorems of functional analysis. Approximation theory-interpolation theoty,best approximation theory. General iterative process and its application. Algorithms of basic iterative methods for solving systems of nonlinear equations. One-step stationary iterative methods. Embeddings methods. Multistep methods. Minimization methods- gradient methods,conjugate gradient method, Gauss-Newton method. Spaces of splines,dimension,defect,B-splines.
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
  • MARČUK, Gurij Ivanovič. Metody numerické matematiky. Vyd. 1. Praha: Academia, 1987, 528 s. URL info
Assessment methods (in Czech)
Přednáška. Zkouška ústní.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.

M9140 Theoretical Numerical Analysis

Faculty of Science
Autumn 2005
Extent and Intensity
2/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivanka Horová, CSc.
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Applied Mathematics)
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. In this course the general theory of iterative processes is built. Further more minimization methods are studied because it is natural to transfer the problem of solving a system to the problem of minimization of a certain functional. Splines are also very important tool of applied mathematics and their general construction can be described in terms of functional analysis. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods.
Syllabus
  • Survey of basic concepts and theorems of functional analysis. Approximation theory-interpolation theoty,best approximation theory. General iterative process and its application. Algorithms of basic iterative methods for solving systems of nonlinear equations. One-step stationary iterative methods. Embeddings methods. Multistep methods. Minimization methods- gradient methods,conjugate gradient method, Gauss-Newton method. Spaces of splines,dimension,defect,B-splines.
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
  • MARČUK, Gurij Ivanovič. Metody numerické matematiky. Vyd. 1. Praha: Academia, 1987, 528 s. URL info
Assessment methods (in Czech)
Přednáška. Zkouška ústní.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.

M9140 Theoretical Numerical Analysis

Faculty of Science
Autumn 2004
Extent and Intensity
2/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivanka Horová, CSc.
Timetable
Thu 10:00–11:50 N41
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. In this course the general theory of iterative processes is built. Further more minimization methods are studied because it is natural to transfer the problem of solving a system to the problem of minimization of a certain functional. Splines are also very important tool of applied mathematics and their general construction can be described in terms of functional analysis. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods.
Syllabus
  • Survey of basic concepts and theorems of functional analysis. Approximation theory-interpolation theoty,best approximation theory. General iterative process and its application. Algorithms of basic iterative methods for solving systems of nonlinear equations. One-step stationary iterative methods. Embeddings methods. Multistep methods. Minimization methods- gradient methods,conjugate gradient method, Gauss-Newton method. Spaces of splines,dimension,defect,B-splines.
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
  • MARČUK, Gurij Ivanovič. Metody numerické matematiky. Vyd. 1. Praha: Academia, 1987, 528 s. URL info
Assessment methods (in Czech)
Přednáška. Zkouška ústní.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught once in two years.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.

M9140 Theoretical Numerical Analysis

Faculty of Science
Autumn 2003
Extent and Intensity
2/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivanka Horová, CSc.
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Applied Mathematics)
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. In this course the general theory of iterative processes is built. Further more minimization methods are studied because it is natural to transfer the problem of solving a system to the problem of minimization of a certain functional. Splines are also very important tool of applied mathematics and their general construction can be described in terms of functional analysis. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods.
Syllabus
  • Survey of basic concepts and theorems of functional analysis. Approximation theory-interpolation theoty,best approximation theory. General iterative process and its application. Algorithms of basic iterative methods for solving systems of nonlinear equations. One-step stationary iterative methods. Embeddings methods. Multistep methods. Minimization methods- gradient methods,conjugate gradient method, Gauss-Newton method. Spaces of splines,dimension,defect,B-splines.
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
  • MARČUK, Gurij Ivanovič. Metody numerické matematiky. Vyd. 1. Praha: Academia, 1987, 528 s. URL info
Assessment methods (in Czech)
Přednáška. Zkouška ústní.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.

M9140 Theoretical Numerical Analysis

Faculty of Science
Autumn 2002
Extent and Intensity
2/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivanka Horová, CSc.
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Applied Mathematics)
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. In this course the general theory of iterative processes is built. Further more minimization methods are studied because it is natural to transfer the problem of solving a system to the problem of minimization of a certain functional. Splines are also very important tool of applied mathematics and their general construction can be described in terms of functional analysis. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods.
Syllabus
  • Survey of basic concepts and theorems of functional analysis. Approximation theory-interpolation theoty,best approximation theory. General iterative process and its application. Algorithms of basic iterative methods for solving systems of nonlinear equations. One-step stationary iterative methods. Embeddings methods. Multistep methods. Minimization methods- gradient methods,conjugate gradient method, Gauss-Newton method. Spaces of splines,dimension,defect,B-splines.
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
  • MARČUK, Gurij Ivanovič. Metody numerické matematiky. Vyd. 1. Praha: Academia, 1987, 528 s. URL info
Assessment methods (in Czech)
Přednáška. Zkouška ústní.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught once in two years.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.

M9140 Theoretical Numerical Analysis

Faculty of Science
Autumn 2024

The course is not taught in Autumn 2024

Extent and Intensity
2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
In-person direct teaching
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods. Student will be able to understand modern methods of numerical analysis.
Learning outcomes
Student obtains a universal view to numerical mathematics and will be able to apply modern numerical methods in practise
Syllabus
  • Survey of basic concepts and theorems of functional analysis
  • Approximation theory-interpolation theoRy,best approximation theory, best approximation in inner spaces
  • Pseudometric spaces, a general fixed point theorem in pseudometric spaces and its application
  • Convergence factors and their relations
  • Differential calculus for nonlinear operators, Newton's method in a Banach space
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
Teaching methods
Lecture: 2 hours weekly, theoretical preparation
Assessment methods
Lecture. Oral exam.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.

M9140 Theoretical Numerical Analysis

Faculty of Science
Autumn 2023

The course is not taught in Autumn 2023

Extent and Intensity
2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods. Student will be able to understand modern methods of numerical analysis.
Learning outcomes
Student obtains a universal view to numerical mathematics and will be able to apply modern numerical methods in practise
Syllabus
  • Survey of basic concepts and theorems of functional analysis
  • Approximation theory-interpolation theoRy,best approximation theory, best approximation in inner spaces
  • Pseudometric spaces, a general fixed point theorem in pseudometric spaces and its application
  • Convergence factors and their relations
  • Differential calculus for nonlinear operators, Newton's method in a Banach space
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
Teaching methods
Lecture: 2 hours weekly, theoretical preparation
Assessment methods
Lecture. Oral exam.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.

M9140 Theoretical Numerical Analysis

Faculty of Science
Autumn 2022

The course is not taught in Autumn 2022

Extent and Intensity
2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods. Student will be able to understand modern methods of numerical analysis.
Learning outcomes
Student obtains a universal view to numerical mathematics and will be able to apply modern numerical methods in practise
Syllabus
  • Survey of basic concepts and theorems of functional analysis
  • Approximation theory-interpolation theoRy,best approximation theory, best approximation in inner spaces
  • Pseudometric spaces, a general fixed point theorem in pseudometric spaces and its application
  • Convergence factors and their relations
  • Differential calculus for nonlinear operators, Newton's method in a Banach space
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
Teaching methods
Lecture: 2 hours weekly, theoretical preparation
Assessment methods
Lecture. Oral exam.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.

M9140 Theoretical Numerical Analysis

Faculty of Science
autumn 2021

The course is not taught in autumn 2021

Extent and Intensity
2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods. Student will be able to understand modern methods of numerical analysis.
Learning outcomes
Student obtains a universal view to numerical mathematics and will be able to apply modern numerical methods in practise
Syllabus
  • Survey of basic concepts and theorems of functional analysis
  • Approximation theory-interpolation theoRy,best approximation theory, best approximation in inner spaces
  • Pseudometric spaces, a general fixed point theorem in pseudometric spaces and its application
  • Convergence factors and their relations
  • Differential calculus for nonlinear operators, Newton's method in a Banach space
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
Teaching methods
Lecture: 2 hours weekly, theoretical preparation
Assessment methods
Lecture. Oral exam.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.

M9140 Theoretical Numerical Analysis

Faculty of Science
Autumn 2019

The course is not taught in Autumn 2019

Extent and Intensity
2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods. Student will be able to understand modern methods of numerical analysis.
Learning outcomes
Student obtains a universal view to numerical mathematics and will be able to apply modern numerical methods in practise
Syllabus
  • Survey of basic concepts and theorems of functional analysis
  • Approximation theory-interpolation theoRy,best approximation theory, best approximation in inner spaces
  • Pseudometric spaces, a general fixed point theorem in pseudometric spaces and its application
  • Convergence factors and their relations
  • Differential calculus for nonlinear operators, Newton's method in a Banach space
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
Teaching methods
Lecture: 2 hours weekly, theoretical preparation
Assessment methods
Lecture. Oral exam.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.

M9140 Theoretical Numerical Analysis I

Faculty of Science
autumn 2017

The course is not taught in autumn 2017

Extent and Intensity
2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods. Student will be able to understand modern methods of numerical analysis.
Syllabus
  • Survey of basic concepts and theorems of functional analysis
  • Approximation theory-interpolation theoRy,best approximation theory, best approximation in inner spaces
  • Pseudometric spaces, a general fixed point theorem in pseudometric spaces and its application
  • Convergence factors and their relations
  • Differential calculus for nonlinear operators, Newton's method in a Banach space
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
Teaching methods
Lecture: 2 hours weekly, theoretical preparation
Assessment methods
Lecture. Oral exam.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.

M9140 Theoretical Numerical Analysis I

Faculty of Science
Autumn 2015

The course is not taught in Autumn 2015

Extent and Intensity
2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods. Student will be able to understand modern methods of numerical analysis.
Syllabus
  • Survey of basic concepts and theorems of functional analysis
  • Approximation theory-interpolation theoRy,best approximation theory, best approximation in inner spaces
  • Pseudometric spaces, a general fixed point theorem in pseudometric spaces and its application
  • Convergence factors and their relations
  • Differential calculus for nonlinear operators, Newton's method in a Banach space
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
Teaching methods
Lecture: 2 hours weekly, theoretical preparation
Assessment methods
Lecture. Oral exam.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.

M9140 Theoretical Numerical Analysis I

Faculty of Science
Autumn 2013

The course is not taught in Autumn 2013

Extent and Intensity
2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Supplier department: Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods. Student will be able to understand modern methods of numerical analysis.
Syllabus
  • Survey of basic concepts and theorems of functional analysis
  • Approximation theory-interpolation theoRy,best approximation theory, best approximation in inner spaces
  • Pseudometric spaces, a general fixed point theorem in pseudometric spaces and its application
  • Convergence factors and their relations
  • Differential calculus for nonlinear operators, Newton's method in a Banach space
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
Teaching methods
Lecture: 2 hours weekly, theoretical preparation
Assessment methods
Lecture. Oral exam.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.

M9140 Theoretical Numerical Analysis I

Faculty of Science
Autumn 2011

The course is not taught in Autumn 2011

Extent and Intensity
2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is offered to students of any study field.
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods.
Syllabus
  • Survey of basic concepts and theorems of functional analysis
  • Approximation theory-interpolation theoRy,best approximation theory, best approximation in inner spaces
  • Pseudometric spaces, a general fixed point theorem in pseudometric spaces and its application
  • Convergence factors and their relations
  • Differential calculus for nonlinear operators, Newton's method in a Banach space
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
Teaching methods
Lecture: 2 hours weekly, theoretical preparation
Assessment methods
Lecture. Oral exam.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.

M9140 Theoretical Numerical Analysis I

Faculty of Science
Autumn 2011 - acreditation

The information about the term Autumn 2011 - acreditation is not made public

Extent and Intensity
2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Applied Mathematics)
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods.
Syllabus
  • Survey of basic concepts and theorems of functional analysis
  • Approximation theory-interpolation theoRy,best approximation theory, best approximation in inner spaces
  • Pseudometric spaces, a general fixed point theorem in pseudometric spaces and its application
  • Convergence factors and their relations
  • Differential calculus for nonlinear operators, Newton's method in a Banach space
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
Teaching methods
Lecture: 2 hours weekly, theoretical preparation
Assessment methods
Lecture. Oral exam.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.

M9140 Theoretical Numerical Analysis I

Faculty of Science
Autumn 2010 - only for the accreditation
Extent and Intensity
2/0. 2 credit(s) (příf plus uk k 1 zk 2 plus 1 > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Applied Mathematics)
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods.
Syllabus
  • Survey of basic concepts and theorems of functional analysis
  • Approximation theory-interpolation theoRy,best approximation theory, best approximation in inner spaces
  • Pseudometric spaces, a general fixed point theorem in pseudometric spaces and its application
  • Convergence factors and their relations
  • Differential calculus for nonlinear operators, Newton's method in a Banach space
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
Teaching methods
Lecture: 2 hours weekly, theoretical preparation
Assessment methods
Lecture. Oral exam.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2007 - for the purpose of the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.

M9140 Theoretical Numerical Analysis I

Faculty of Science
Autumn 2007 - for the purpose of the accreditation
Extent and Intensity
2/0. 2 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivanka Horová, CSc.
Prerequisites
Basic numerical methods of mathematical analysis and linear algebra. Grounding of functional analysis.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
  • Mathematics (programme PřF, M-MA, specialization Applied Mathematics)
Course objectives
In modern numerical mathematics there is a distinct effort to an abstract approach based on functional analysis.Here,functional analysis is connecting element between "pure" and "applied"mathematics and wipes the difference between these two "branches" of mathematics. In this course the general theory of iterative processes is built. Further more minimization methods are studied because it is natural to transfer the problem of solving a system to the problem of minimization of a certain functional. Splines are also very important tool of applied mathematics and their general construction can be described in terms of functional analysis. This course comes on the top of preceding courses of numerical mathematics and offers universal view to studied numerical methods.
Syllabus
  • Survey of basic concepts and theorems of functional analysis. Approximation theory-interpolation theoty,best approximation theory. General iterative process and its application. Algorithms of basic iterative methods for solving systems of nonlinear equations. One-step stationary iterative methods. Embeddings methods. Multistep methods. Minimization methods- gradient methods,conjugate gradient method, Gauss-Newton method. Spaces of splines,dimension,defect,B-splines.
Literature
  • ATKINSON, Kendall and Weimin HAN. Theoretical Numerical Analysis. New-York: Springer-Verlag, 2001, 450 pp. Texts in Applied Mathematics. ISBN 0-387-95142-3. info
  • ORTEGA, James M. and Werner C. RHEINBOLDT. Iterative Solution of Nonlinear Equations in Several Variables. 1st ed. New York - London: Academic Press, 1970, 572 pp. Computer Science and Applied Mathematics. info
  • VASILENKO, Vladimir Aleksandrovič. Splajn-funkcii : teorija, algoritmy, programmy. Novosibirsk: Nauka, 1983, 210 s. info
  • MARČUK, Gurij Ivanovič. Metody numerické matematiky. Vyd. 1. Praha: Academia, 1987, 528 s. URL info
Assessment methods (in Czech)
Přednáška. Zkouška ústní.
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course is taught annually.
The course is taught: every week.
The course is also listed under the following terms Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011 - acreditation, Autumn 2012, Autumn 2014, Autumn 2016, Autumn 2018, Autumn 2020.
  • Enrolment Statistics (recent)