A study on multivariate interpolation by increasingly flat kernel functions

Yeon Ju Lee; Charles A. Micchelli; Jungho Yoon

doi:10.1016/j.jmaa.2015.02.006

A study on multivariate interpolation by increasingly flat kernel functions

Yeon Ju Lee, Charles A. Micchelli, Jungho Yoon

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

In this paper, we improve upon some observations made in recent papers on the subject of increasingly flat interpolation. We shall establish that the corresponding Lagrange functions converge both for a finite set of functions (collocation matrix) and also for kernels (Fredholm matrix). In our analysis, we use a finite Maclaurin expansion of a multivariate function with remainder and some additional matrix theoretic facts.

Original language	English
Pages (from-to)	74-87
Number of pages	14
Journal	Journal of Mathematical Analysis and Applications
Volume	427
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2015.02.006
State	Published - 1 Jul 2015

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Inc.

Keywords

Cauchy-Binet formula
Collocation matrix
L'Hospital's rule
Multivariate kernel interpolation
Radial basis function
Wronskian

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10.1016/j.jmaa.2015.02.006

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abstract = "In this paper, we improve upon some observations made in recent papers on the subject of increasingly flat interpolation. We shall establish that the corresponding Lagrange functions converge both for a finite set of functions (collocation matrix) and also for kernels (Fredholm matrix). In our analysis, we use a finite Maclaurin expansion of a multivariate function with remainder and some additional matrix theoretic facts.",

keywords = "Cauchy-Binet formula, Collocation matrix, L'Hospital's rule, Multivariate kernel interpolation, Radial basis function, Wronskian",

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AU - Micchelli, Charles A.

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AB - In this paper, we improve upon some observations made in recent papers on the subject of increasingly flat interpolation. We shall establish that the corresponding Lagrange functions converge both for a finite set of functions (collocation matrix) and also for kernels (Fredholm matrix). In our analysis, we use a finite Maclaurin expansion of a multivariate function with remainder and some additional matrix theoretic facts.

KW - Cauchy-Binet formula

KW - Collocation matrix

KW - L'Hospital's rule

KW - Multivariate kernel interpolation

KW - Radial basis function

KW - Wronskian

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JF - Journal of Mathematical Analysis and Applications

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ER -

A study on multivariate interpolation by increasingly flat kernel functions

Abstract

Bibliographical note

Keywords

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