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Factorization, symmetrization, and truncated transformation of radial basis function-GA stabilized Gaussian radial basis functions
Publikationstyp
Journal Article
Date Issued
2019
Sprache
English
Author(s)
Institut
TORE-URI
Volume
40
Issue
2
Start Page
517
End Page
541
Citation
SIAM Journal on Matrix Analysis and Applications 2 (40): 517-541 (2019)
Publisher DOI
Scopus ID
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.
Subjects
Factorization
Ill-conditioning
Kernel-based interpolation
Radial basis function
Stable
Symmetrization
Truncation