M4180 Numerical Methods I

Faculty of Science
Spring 2008 - for the purpose of the accreditation
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: zk (examination).
Teacher(s)
prof. RNDr. Ivanka Horová, CSc. (lecturer)
doc. Mgr. Kamila Hasilová, Ph.D. (seminar tutor)
doc. Mgr. Jan Koláček, Ph.D. (seminar tutor)
RNDr. Martin Tajovský (seminar tutor)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivanka Horová, CSc.
Prerequisites
Differential calculus of functions of one and more variables.Basic knoledge of linear algebra-theory of matrices and solving systems of linear equations.
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
there are 8 fields of study the course is directly associated with, display
Course objectives
This course together with the course Numerical Methods II provides complete explanation of numerical mathematics as the separate scientific discipline.The students are acquainted with methods of finding roots of functions including special methods for finding roots of polynomials.The major part of these methods is based on the Banach fixed point principle.This principle is also a basis for iterative methods for solving of systems of linear equations which are also included in this course.The methods for special matrices are also added to the classical direct methods. Stability of algorithms and conditioning of problems are also treated of. The accent is put on the algorithmization and computer implementation. Some examples with graphical outputs help to explain even some difficult parts.
Syllabus
  • Error analysis Solving of nonlinear equations-iterative methods,their order and convergence,Newton method,secant method,regula falsi method, Steffensen method,Müller method. Solving of systems of nonlinear equations-Newton method,Seidel method. Roots of polynomials-Sturm theorem,application of Newton method, finding all roots of polynomials,Bairstow method. Direct methods for solving systems of linear equations-Gaussian elimination,LU decomposition,Cholesky method,Crout method,backward error analysis,stability of algorithms and conditioning of problems. Iterative methods for solving of systems of linear equations- principle of a construction of iterative methods,convergence theorems, Jacobi method,Gauss-Seidel method,relaxation methods.
Literature
  • STOER, J. and R. BULIRSCH. Introduction to numerical analysis. 1st ed. New York - Heidelberg - Berlin: Springer-Verlag, 1980, 609 pp. IX. ISBN 0-387-90420-4. info
  • RALSTON, Anthony. Základy numerické matematiky. Translated by Milan Práger - Emil Vitásek. České vyd. 2. Praha: Academia, 1978, 635 s. info
  • HOROVÁ, Ivana. Numerické metody. 1st ed. Brno: Masarykova univerzita, 1999, 230 pp. ISBN 80-210-2202-7. info
  • DATTA, Biswa Nath. Numerical linear algebra and applications. Pacific Grove: Brooks/Cole publishing company, 1994, xxii, 680. ISBN 0-534-17466-3. info
  • VITÁSEK, Emil. Numerické metody. Vyd. 1. Praha: SNTL - Nakladatelství technické literatury, 1987, 512 s. URL info
  • MÍKA, Stanislav. Numerické metody algebry. 2. vyd. Praha: SNTL - Nakladatelství technické literatury, 1985, 169 s. URL info
  • HOROVA, Ivana and Jiří ZELINKA. Numerické metody (Numerical Methods). 2nd ed. Brno: Masarykova univerzita v Brně, 2004, 294 pp. 3871/Př-2/04-17/31. ISBN 80-210-3317-7. info
Assessment methods (in Czech)
Výuka :přednáška,cvičení v počítačové učebně.Pro získání zápočtu musí student vypracovat zápočtový příklad v MATLABu. Zkouška :písemná,(ústní).
Language of instruction
Czech
Follow-Up Courses
Further Comments
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Spring 2011 - only for the accreditation, Spring 2003, Spring 2004, Spring 2005, Spring 2006, Spring 2007, Spring 2008, Spring 2009, Spring 2010, Spring 2011, Spring 2012, spring 2012 - acreditation, Spring 2013, Spring 2014, Spring 2015, Spring 2016, Spring 2017, spring 2018, Spring 2019, Spring 2020, Spring 2021, Spring 2022, Spring 2023, Spring 2024, Spring 2025.