Approximation by piecewise constants on convex partitions

O. Davydov

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Abstract

We show that the saturation order of piecewise constant approximation in Lp norm on convex partitions with N cells is N−2/(d+1), where d is the number of variables. This order is achieved for any on a partition obtained by a simple algorithm involving an anisotropic subdivision of a uniform partition. This improves considerably the approximation order N−1/d achievable on isotropic partitions. In addition we show that the saturation order of piecewise linear approximation on convex partitions is N−2/d, the same as on isotropic partitions.
Original languageEnglish
Pages (from-to)346-352
Number of pages7
JournalJournal of Approximation Theory
Volume164
Issue number2
DOIs
Publication statusPublished - 2012

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Keywords

  • approximation
  • convex partitions
  • mathematical analysis
  • isotropic partitions

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