Anisotropic Radial Basis Functions on optimized Mahalanobis-Norms
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TALK
Lars-Benjamin Maier (University of Eichstätt-Ingolstadt, Germany), 19 March 2012, 9:15 am, S2 0354
Anisotropic Radial Basis Functions on optimized Mahalanobis-Norms
In this talk, we are going to give a short introdution into new developments of research in the field of radial basis function interpolation and approximation, a widely used technique in approximation, data analysis and surface reconstruction.
After a formal introduction to the general issue, we are especially concerned with problems where the given data is extremely scattered, i.e. not very uniform and full of gaps or holes which we would like to cover. Therefore, so called Mahalanobis-Norms (non euclidean sclar product induced norms) are used to make the radial basis functions 'anisotropic', and two algorithms as well as test results are presented. We conclude with some new methods of optimized discrete least squares approximation, where we present methods of optimaly choosing the function space used for approximation via optimizing the Mahalanobis-Norms in the basis functions.