Multivariate Interpolation Using Linear Combinations of Translates of a Conditionally Positive Definite Function

Abstract

In this paper, we discuss “cardinal” as well as “infinite scattered data” interpolation using finite linear combination of translates of a conditionally positive definite function. We prove that for a subclass of such functions, the cardinal interpolation operators are bounded and invertible on lp, 1 ≤ p≤ I ∞.In some special cases, including “Hardy's multiquadrics” and “The Thin Plate Spline,” we show that the scattered data interpolation operators are bounded and invertible on l2.

Department(s)

Mathematics

Document Type

Article

DOI

https://doi.org/10.1080/01630569308816527

Publication Date

1-1-1993

Journal Title

Numerical Functional Analysis and Optimization

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