Approximation with Kernel Methods

Spezielle Aspekte der Numerik

Dozent

Dr. Gabriele Santin, Prof. Dr. Bernard Haasdonk

 

Beginn

First lecture 16.10.2017

Zeitraum

16.10.2017 - 7.2.2018

Zeit/Ort

Mon. 14:00-15:30, Wed. 14:00-15:30 PWR 57, 7.122

Übungen

Wed. 14:00-15:30 (first exercise 25.10.2017) PWR 57, 7.122

Ilias-Link

Ilias

Inhalt

Kernel methods represent an interesting class of techniques which have successfully been used in different approximation tasks during the last decades. First, the lecture will provide background of kernel methods and the connection to the corresponding function spaces. Particularly, positive definite symmetric kernels can be related to so called Reproducing Kernel Hilbert Spaces (RKHS). Examples of such functions are the Gaussian kernel or more general kernels obtained from Radial Basis Functions (RBF). We then consider the following special problems and numerical techniques:

  1. Approximation of scattered data (Greedy procedures, Regression)
  2. Pattern recognition (Classification, Support Vector Machines (SVM))
  3. Numerical approximation of PDEs by collocation. 

This lecture provides a good basis for MSc/BSc theses or student assistant jobs in the research group.

Literatur

Ilias

Lernziele, Prüfung

Ilias

Curricula

M.Sc. Mathematik, B.Sc. Mathematik, SimTech

Voraussetzungen

Numerische Mathematik I

Leistungspunkte

6

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