A new stable basis for RBF approximation

Gabriele Santin

doi:10.1016/j.cam.2013.03.048

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arXiv · 1210.1682

A new stable basis for RBF approximation

Gabriele Santin

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Abstract

It's well know that Radial Basis Function approximants suffers of bad conditioning if the simple basis of translates is used. A recent work of M.Pazouki and R.Schaback gives a quite general way to build stable, orthonormal bases for the native space based on a factorization of the kernel matrix A. Starting from that setting we describe a particular orthonormal basis that arises from a weighted singular value decomposition of A. This basis is related to a discretization of the compact operator which leads to the so-called eigenbasis, and provides a connection with it. We give convergence estimates and stability bound for the interpolation and the discrete least-squares approximation based on this basis, which involves the eigenvalues of such an operator.

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Gabriele Santin. 2012-10-05. A new stable basis for RBF approximation. https://doi.org/10.1016/j.cam.2013.03.048

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