On quasi-interpolation by radial basis functions with scattered centres

M. D. Buhmann, N. Dyn, D. Levin

Research output: Contribution to journalArticlepeer-review


Approximation by radial basis functions with "quasi-uniformly" distributed centres in Rd is discussed. A construction of new polynomially decaying functions that span the approximation space is presented and the properties of the quasi-interpolation operator with these functions are investigated. It is shown that the quasi-interpolant reproduces polynomials and gives approximation orders identical to those in the uniform square-grid case.

Original languageEnglish
Pages (from-to)239-254
Number of pages16
JournalConstructive Approximation
Issue number2
StatePublished - Jun 1995


  • AMS classification: Primary 41A15, 41A63, 41A25, 65D15, Secondary 41A30, 65D07, 65D10
  • Multivariate approximation
  • Quasi-interpolation
  • Radial basis functions
  • Scattered data


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