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Multivariate interpolation in odd-dimensional euclidean spaces using multiquadrics

Authors:

M. D. Buhmann

Affiliation:

1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, CB3 9EW, Cambridge, England

Abstract:

Let $varphi (r) = sqrt {r^2 + c^2 }$ or $varphi (r) = 1/sqrt {r^2 + c^2 }$ . Givenf:ⁿ rarr

, we establish convergence orders of interpolation where the cardinal functionx withx(j)= delta

_0j is a linear combination of integer shifts, of a fast decaying function

$psi (x) = mathop Sigma limits_{j in N} mu _i varphi (\|\|x - j\|\|),x in R^n ,$

Keywords:	KeywordHeading" > and phrases Multivariate interpolation Multivariate approximation Radial basis functions Orders of convergence Polynomial precision Multiquadrics
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