Polynomial degree reduction in the discrete L2-norm equals best Euclidean approximation of h-Bézier coefficients

Rachid Ait-Haddou

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We show that the best degree reduction of a given polynomial P from degree n to m with respect to the discrete (Formula presented.)-norm is equivalent to the best Euclidean distance of the vector of h-Bézier coefficients of P from the vector of degree raised h-Bézier coefficients of polynomials of degree m. Moreover, we demonstrate the adequacy of h-Bézier curves for approaching the problem of weighted discrete least squares approximation. Applications to discrete orthogonal polynomials are also presented. © 2015 Springer Science+Business Media Dordrecht
Original languageEnglish (US)
Pages (from-to)1-14
Number of pages14
JournalBIT Numerical Mathematics
Volume56
Issue number1
DOIs
StatePublished - Jun 4 2015

ASJC Scopus subject areas

  • Computational Mathematics
  • Software
  • Applied Mathematics
  • Computer Networks and Communications

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