A study on multivariate interpolation by increasingly flat kernel functions

Yeon Ju Lee, Charles A. Micchelli, Jungho Yoon

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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
Issue number1
StatePublished - 1 Jul 2015

Bibliographical note

Funding Information:
The authors are grateful to the anonymous referee for the valuable suggestions on this paper. Jungho Yoon was supported by Priority Research Centers Program 2009-0093827 through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology . C. Micchelli is supported in part by the US National Science Foundation under grant DMS-1115523 .

Publisher Copyright:
© 2015 Elsevier Inc.


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


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