Polynomials and their Potential Theory for Gaussian Radial Basis Function Interpolation

Author(s)Driscoll, Tobin A.
Author(s)Platte, Rodrigo B.
Date Accessioned2004-12-21T16:37:10Z
Date Available2004-12-21T16:37:10Z
Publication Date2004
AbstractWe explore a connection between Gaussian radial basis functions and polynomials. Using standard tools of potential theory, we find that these radial functions are susceptible to the Runge phenomenon, not only in the limit of increasingly flat functions, but also in the finite shape parameter case. We show that there exist interpolation node distributions that prevent such phenomena and allow stable approximations. Using polynomials also provides an explicit interpolation formula that avoids the difficulties of inverting interpolation matrices, without imposing restrictions on the shape parameter or number of points.en
SponsorSupported by NSF DMS-0104229
Extent667615 bytes
MIME typeapplication/pdf
URLhttp://udspace.udel.edu/handle/19716/205
Languageen_US
PublisherDepartment of Mathematical Sciencesen
Part of SeriesTechnical Report: 2004-01
KeywordsGaussian radial basis functionsen
KeywordsRBFen
Keywordspotential theoryen
KeywordsRunge phenomenonen
Keywordsconvergenceen
Keywordsstabilityen
dc.subject.classificationAMS: 65D05, 41A30
TitlePolynomials and their Potential Theory for Gaussian Radial Basis Function Interpolationen
TypeTechnical Reporten
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