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. |
URI: | http://hdl.handle.net/11420/3272 | ISSN: | 0895-4798 | Journal: | SIAM journal on matrix analysis and applications | Institute: | Mathematik E-10 | Document Type: | Article |
Appears in Collections: | Publications without fulltext |
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