Universität Wien

250005 VO Approximation Theory (2022S)

6.00 ECTS (4.00 SWS), SPL 25 - Mathematik
Moodle

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Details

Language: English

Examination dates

Lecturers

Classes (iCal) - next class is marked with N

  • Wednesday 02.03. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 03.03. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 09.03. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 10.03. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 16.03. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 17.03. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 23.03. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 24.03. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 30.03. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 31.03. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 06.04. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 07.04. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 27.04. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 28.04. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 04.05. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 05.05. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 11.05. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 12.05. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 18.05. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 19.05. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 25.05. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 01.06. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 02.06. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 08.06. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 09.06. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 15.06. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 22.06. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 23.06. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Wednesday 29.06. 11:30 - 13:00 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Thursday 30.06. 13:15 - 14:45 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

The basic goal of approximation theory is the approximation of a (complicated) function by a function with a simpler structure. A typical question is how well a smooth function can be approximated by a polynomial of given degree. A modern version is this problem is the approximation of an unknown function from given data (versions of this problem are now often identified as data science). Approximation theory is a compagnon of numerical analysis. Many times it has been considered finished or "dead", but each new fashion (wavelet theory in the 1990s, compressed sensing in the 2000s, or currently machine learning and data science call again on the conceptual framework of approximation theory. The course will give an overview of classical approximation theory with an attempt to lead up to contemporary issues.
Preliminary plan: approximation in linear spaces, polynomial approximation, approximation order, shift-invariant spaces, non-linear approximation, approximation numbers.
Prerequisites: some functional analysis and numerical analysis from the bachelor courses, some knowledge of Fourier series.

Assessment and permitted materials

Oral exam. (If the number of students exceeds 25, I will consider a written exam)

Minimum requirements and assessment criteria

Satisfactory answer to questions of oral exam.

Examination topics

Entire course material including problems and exercises discussed during the course.

Reading list

T. Sauer: Approximationstheorie (Vorlesungsskript), Universität Gießen, https://www.fim.uni-passau.de/fileadmin/files/lehrstuhl/sauer/geyer/Approx.pdf

E. W. Cheney: Introduction to Approximation Theory, 2nd edition, Chelsea, New York, 1982.

Cheney, Ward; Light, Will A course in approximation theory.

Iske, Armin Approximation theory and algorithms for data analysis.

M. Powell, "Approximation theory and methods"

V. Temlyakov, "Multivariate approximation"

L. N. Trefethen, "Approximation theory and approximation practice", SIAM

Association in the course directory

MANV; MAMV;

Last modified: Th 30.05.2024 00:15