Constructive Approximation

, Volume 3, Issue 1, pp 239–248

Free multivariate splines

  • Ronald A. DeVore
  • Vasil A. Popov

DOI: 10.1007/BF01890567

Cite this article as:
DeVore, R.A. & Popov, V.A. Constr. Approx (1987) 3: 239. doi:10.1007/BF01890567


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


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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