Universität Wien

250078 VO Theory of approximation (2008W)

7.00 ECTS (4.00 SWS), SPL 25 - Mathematik

Um eine Überschneidung mit der Vorlesung "Optimierung" von H. Schichl zu vermeiden, wird die Vorlesung am Donnerstag voraussichtlich von 10:30 - 12:00 abgehalten, "Optimierung" am Donnerstag auf 9:00 - 10:30 vorverlegt.

Details

Language: German

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 07.10. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Thursday 09.10. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Tuesday 14.10. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Thursday 16.10. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Tuesday 21.10. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Thursday 23.10. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Tuesday 28.10. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Thursday 30.10. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Tuesday 04.11. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Thursday 06.11. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Tuesday 11.11. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Thursday 13.11. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Tuesday 18.11. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Thursday 20.11. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Tuesday 25.11. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Thursday 27.11. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Tuesday 02.12. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Thursday 04.12. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Tuesday 09.12. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Thursday 11.12. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Tuesday 16.12. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Thursday 18.12. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Thursday 08.01. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Tuesday 13.01. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Thursday 15.01. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Tuesday 20.01. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Thursday 22.01. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Tuesday 27.01. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II
  • Thursday 29.01. 10:15 - 11:45 Seminarraum 2A310 3.OG UZA II

Information

Aims, contents and method of the course

Approximation theory forms a bridge between analysis and computation.
To find the solution to a differential equation, say, we approximate
it by polynomials, trigonometric polynomials, splines, wavelets, etc.
Some typical problems: How well can a (periodic) function be
approximated by a trigonometric polynomial? What does the rate of
approximation say about the properties of the original function?
When does a best approximation exist and how to find it?

This course will give an introduction to approximation theory.
The main part of the semester will be devoted to classical
approximation theory, towards the end will be discussed some new
developments (non-linear approximation)

Assessment and permitted materials

Exam (oral),
Hand in of exercises (voluntary)

Minimum requirements and assessment criteria

Planned topics:
1. Polynomial approximation and density theorems
2. Approximation in linear spaces
3. Trigonometric polynomials, the Jackson-Bernstein theorems
4. Rational functions
5. Non-linear Approximation
6. Wavelets and splines

Examination topics

Prerequisites: Analysis 1 and 2, linear Algebra, basics on Fourier series, metric spaces, and inner product spaces.

Reading list

Cheney "Approximation theory" (1981)
G.G. Lorentz "Approximation of functions"
Weitere Literatur gibt es zu Beginn der Vorlesung.

Association in the course directory

MANV, MAMV

Last modified: Sa 02.04.2022 00:24