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Best polynomial degree reduction on q-lattices with applications to q-orthogonal polynomials
Journal article   Peer reviewed

Best polynomial degree reduction on q-lattices with applications to q-orthogonal polynomials

Rachid Ait-Haddou, Ron Goldman and Rachid Ait-Haldou
Applied mathematics and computation, Vol.266, pp.267-276
01/09/2015
DOI: https://doi.org/10.1016/j.amc.2015.05.068

Abstract

(ω|q)-Bernstein bases Degree reduction Discrete least squares Little q-Legendre polynomials q-Bernstein bases q-Hahn polynomials
•We study the best polynomial degree reduction with respect to the q-L2-norm.•We study a finite analogue with respect to finite q-lattices.•We present applications to q-orthogonal polynomials. We show that a weighted least squares approximation of q-Bézier coefficients provides the best polynomial degree reduction in the q-L2-norm. We also provide a finite analogue of this result with respect to finite q-lattices and we present applications of these results to q-orthogonal polynomials.

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