Multivariate quasi-interpolation schemes for dimension-splitting multiquadric

Leevan LING*

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

19 Citations (Scopus)


In this paper, we extend the multilevel univariate quasi-interpolation formula proposed in [A univariate quasi-multiquadric interpolation with better smoothness, Comput. Math. Appl., in press] to multidimensions using the dimension-splitting multiquadric (DSMQ) basis function approach. Our multivariate scheme is readily preformed on parallel computers. We show that the cost of finding the coefficient of the quasi-interpolant is 3dN on ℝd, and the work of direct evaluation of the quasi-interpolant can be reduced from 11N2 in 2D and 16N2 in 3D to ≈ 2N. A boundary padding technique can be employed to improve accuracy. Numerical results in 2D and 3D are both given.

Original languageEnglish
Pages (from-to)195-209
Number of pages15
JournalApplied Mathematics and Computation
Issue number1
Publication statusPublished - 4 Feb 2005

Scopus Subject Areas

  • Computational Mathematics
  • Applied Mathematics

User-Defined Keywords

  • Dimension-splitting
  • Multidimensional
  • Multilevel
  • Multiquadric (MQ)
  • Multivariate
  • Quasi-interpolation
  • Radial basis function (RBF)


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