Explicit multivariate approximations from cell-average data

Sergio Amat, David Levin, Juan Ruiz-Álvarez, Dionisio F. Yáñez*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Given gridded cell-average data of a smooth multivariate function, we present a constructive explicit procedure for generating a high-order global approximation of the function. One contribution is the derivation of high-order approximations to point-values of the function directly from the cell-average data. The second contribution is the development of univariate B-spline-based high-order quasi-interpolation operators using cell-average data. Multivariate spline quasi-interpolation approximation operators are obtained by tensor product of the univariate operators.

Original languageEnglish
Article number85
JournalAdvances in Computational Mathematics
Issue number6
StatePublished - Dec 2022


  • Cell-average data
  • Explicit approximation
  • Multivariate
  • Quasi-interpolation
  • Splines


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