|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|
Show full item record
checked on Jul 5, 2022
checked on Jun 30, 2022
Add Files to Item
Note about this record
Cite this record
Items in TORE are protected by copyright, with all rights reserved, unless otherwise indicated.