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

Rachid Ait-Haddou; Ron Goldman

doi:10.1016/j.amc.2015.05.068

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

Rachid Ait-Haddou^*
, Ron Goldman

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	267-276
Number of pages	10
Journal	Applied Mathematics and Computation
Volume	266
DOIs	https://doi.org/10.1016/j.amc.2015.05.068
State	Published - 8 Jun 2015
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2015 Elsevier Inc. All rights reserved.

Keywords

(ω|q)-Bernstein bases
Degree reduction
Discrete least squares
Little q-Legendre polynomials
q-Bernstein bases
q-Hahn polynomials

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2015.05.068

Cite this

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title = "Best polynomial degree reduction on q-lattices with applications to q-orthogonal polynomials",

abstract = "We show that a weighted least squares approximation of q-B{\'e}zier 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.",

keywords = "(ω|q)-Bernstein bases, Degree reduction, Discrete least squares, Little q-Legendre polynomials, q-Bernstein bases, q-Hahn polynomials",

author = "Rachid Ait-Haddou and Ron Goldman",

year = "2015",

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day = "8",

doi = "10.1016/j.amc.2015.05.068",

language = "English",

volume = "266",

pages = "267--276",

journal = "Applied Mathematics and Computation",

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T1 - Best polynomial degree reduction on q-lattices with applications to q-orthogonal polynomials

AU - Ait-Haddou, Rachid

AU - Goldman, Ron

PY - 2015/6/8

Y1 - 2015/6/8

N2 - 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.

AB - 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.

KW - (ω|q)-Bernstein bases

KW - Degree reduction

KW - Discrete least squares

KW - Little q-Legendre polynomials

KW - q-Bernstein bases

KW - q-Hahn polynomials

UR - https://www.scopus.com/pages/publications/84930660313

U2 - 10.1016/j.amc.2015.05.068

DO - 10.1016/j.amc.2015.05.068

M3 - Article

AN - SCOPUS:84930660313

SN - 0096-3003

VL - 266

SP - 267

EP - 276

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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