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Vorlesung "Approximation with Kernel Methods" (Spezielle Aspekte der Numerik)

Prof. Dr. Bernard Haasdonk
Zeitraum Mi. 21.10.2015 bis Fr. 5.7.2016
Wed. 11:30-13:00, Fri. 8:00-9:30 (first lecture 21.10.2015) PWR 57, SR 7.122
Wed. 11:30-13:00 (first exercise 28.10.2015) PWR 57, SR 7.122
Ilias-Link https://ilias3.uni-stuttgart.de/goto_Uni_Stuttgart_crs_894030.html

This lecture deals with approximation problems, which can be solved with kernel methods.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 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:

-Kernel based interpolation

-Approximation of scattered data (Greedy procedures, Regression)

-Pattern recognition (classification, Support Vector Machines (SVM))

-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 see ILIAS Site
Curricula MSc Mathematik, SimTech, BSc Mathematik "vorgezogenes Master-Modul", GS Simtech
Basic knowledge in Numerics, e.g. as provided by the BSc lectures Numerische Mathematik 1 + 2. Knowledge in Numerics for PDEs is not required. The course can be taken WITHOUT previous lectures on Partial Differential Equations.

see ILIAS Site


See corresponding ILIAS site for details on content, current announcements, exercises, literature, exam modalities and requirements.