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

7 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

Access to Document

10.1016/j.jmaa.2015.02.006

Cite this

@article{2cc56d23d299435b9e98e8c1eec50d3e,

title = "A study on multivariate interpolation by increasingly flat kernel functions",

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",

author = "Lee, {Yeon Ju} and Micchelli, {Charles A.} and Jungho Yoon",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

year = "2015",

month = jul,

day = "1",

doi = "10.1016/j.jmaa.2015.02.006",

language = "English",

volume = "427",

pages = "74--87",

journal = "Journal of Mathematical Analysis and Applications",

issn = "0022-247X",

publisher = "Academic Press Inc.",

number = "1",

}

TY - JOUR

T1 - A study on multivariate interpolation by increasingly flat kernel functions

AU - Lee, Yeon Ju

AU - Micchelli, Charles A.

AU - Yoon, Jungho

PY - 2015/7/1

Y1 - 2015/7/1

N2 - 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.

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

UR - http://www.scopus.com/inward/record.url?scp=84924050402&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2015.02.006

DO - 10.1016/j.jmaa.2015.02.006

M3 - Article

AN - SCOPUS:84924050402

SN - 0022-247X

VL - 427

SP - 74

EP - 87

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 1

ER -

A study on multivariate interpolation by increasingly flat kernel functions

Abstract

Bibliographical note

Keywords

Access to Document

Fingerprint

Cite this