Making conditionally negative definite radial basis function interpolation well-conditioned by adding cardinal basis functions

A class of basis functions so called well-conditioned RBF (WRBFs) has been introduced. This basis has been manipulated by adding cardinal functions to the conditionally negative definite RBFs of order 1, such as Multiquadric functions 1+(∊r)2 (MQ) and log(1+(∊r)2) (LOG). The condition number of the...

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Bibliographic Details
Published inAin Shams Engineering Journal Vol. 9; no. 4; pp. 2587 - 2598
Main Authors Kazem, Saeed, Chadwick, Edmund A., Hatam, Ali
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.12.2018
Elsevier
Subjects
Cardinal functions
Multiquadrics (MQ)
Radial basis functions
Cardinal functions
Radial basis functions
Multiquadrics (MQ)
65M06
65M20
Online AccessGet full text
ISSN2090-4479
DOI10.1016/j.asej.2017.03.013

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Summary:A class of basis functions so called well-conditioned RBF (WRBFs) has been introduced. This basis has been manipulated by adding cardinal functions to the conditionally negative definite RBFs of order 1, such as Multiquadric functions 1+(∊r)2 (MQ) and log(1+(∊r)2) (LOG). The condition number of the interpolation matrix arising from this basis is of O(N), where N is the number of center nodes. This order is independent of shape parameter and therefore applying this basis functions would recover the ill–posed linear system associated with the order 1 conditionally negative definite RBFs interpolation.
ISSN:2090-4479
DOI:10.1016/j.asej.2017.03.013