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.
  • Enrolment Statistics (Autumn 2005, recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2005/M9140