Publisher DOI: 10.1137/18M119207X
Title: Factorization, symmetrization, and truncated transformation of radial basis function-GA stabilized Gaussian radial basis functions
Language: English
Authors: Le Borne, Sabine  
Keywords: Factorization; Ill-conditioning; Kernel-based interpolation; Radial basis function; Stable; Symmetrization; Truncation
Issue Date: 2019
Source: SIAM Journal on Matrix Analysis and Applications 2 (40): 517-541 (2019)
Abstract (english): 
Radial basis function (RBF) interpolation is a powerful, meshfree tool for function approximation but its direct implementation might suffer from severe ill-conditioning as the shape parameter decreases. We build upon RBF-GA, a stable approach for Gaussian RBFs, and derive its representation in terms of a matrix factorization which can then be generalized to a symmetrized version. This symmetrized version requires fewer function evaluations, yields new insight into the flat limit case, and, combined with diagonal scaling, allows a further reduction of the condition number. We also propose a truncated version of the basis transformation. We conclude with numerical tests to illustrate the performance of all introduced interpolation methods.
ISSN: 0895-4798
Journal: SIAM journal on matrix analysis and applications 
Institute: Mathematik E-10 
Document Type: Article
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