|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)||Journal or Series Name:||SIAM journal on matrix analysis and applications||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.||URI:||http://hdl.handle.net/11420/3272||ISSN:||1095-7162||Institute:||Mathematik E-10||Type:||(wissenschaftlicher) Artikel|
|Appears in Collections:||Publications without fulltext|
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