Constructive Approximation

, Volume 3, Issue 1, pp 239–248 | Cite as

Free multivariate splines

  • Ronald A. DeVore
  • Vasil A. Popov
Article

Abstract

We introduce a definition of free multivariate splines which generalizes the univariate notion of splines with free knots. We then concentrate on the simplest case, piecewise constant functions and characterize some classes of functions which have a prescribed order of approximation inLp by these splines. These characterizations involve the classical Besov spaces.

Key words and phrases

Multivariate approximation Splines with free knots Order of approximation Besov spaces 

AMS classification

41A20 

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References

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Copyright information

© Springer-Verlag New York Inc. 1987

Authors and Affiliations

  • Ronald A. DeVore
    • 1
  • Vasil A. Popov
    • 2
  1. 1.Department of Math. and StatisticsUniversity of South CarolinaColumbiaUSA
  2. 2.Mathematical InstituteBulgarian Academy of ScienceSofiaBulgaria

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