A new stable basis for RBF approximation

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.

Cited by in corpus (12)

• Hybrid Gaussian-cubic radial basis functions for scattered data interpolation
• A stabilized radial basis-finite difference (RBF-FD) method with hybrid kernels
• A trivariate interpolation algorithm using a cube-partition searching procedure
• Partition of unity interpolation using stable kernel-based techniques
• Surrogate assisted active subspace and active subspace assisted surrogate -- A new paradigm for high dimensional structural reliability analysis
• An improved radial basis-pseudospectral method with hybrid Gaussian-cubic kernels
• Approximation of Eigenfunctions in Kernel-based Spaces
• Towards stability of radial basis function based cubature formulas
• Towards stability results for global radial basis function based quadrature formulas
• Approximating basins of attraction for dynamical systems via stable radial bases
• On the constrained mock-Chebyshev least-squares
• A Kernel Method for CT Reconstruction: a Fast Implementation using Circulant Matrices