A study on multivariate interpolation by increasingly flat kernel functions

Yeon Ju Lee, Charles A. Micchelli, Jungho Yoon

Research output: Contribution to journalArticlepeer-review

5 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 languageEnglish
Pages (from-to)74-87
Number of pages14
JournalJournal of Mathematical Analysis and Applications
Volume427
Issue number1
DOIs
StatePublished - 1 Jul 2015

Keywords

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

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