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.
Abstract
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
Key topics
  • 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
Study resources and 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
Approaches, practices, and methods used in teaching
Lecture: 2 hours weekly, theoretical preparation
Method of verifying learning outcomes and course completion requirements
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.
  • Enrolment Statistics (recent)
  • Permalink: https://is.muni.cz/course/sci/autumn2020/M9140