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

Show full item record

Page view(s)

78
Last Week
0
Last month
3
checked on Sep 27, 2020

Google ScholarTM

Check

Add Files to Item

Note about this record

Export

Items in TORE are protected by copyright, with all rights reserved, unless otherwise indicated.