Continuous and discrete best polynomial degree reduction with Jacobi and Hahn weights

Rachid Ait-Haddou

doi:10.1016/j.jat.2016.02.018

Continuous and discrete best polynomial degree reduction with Jacobi and Hahn weights

Rachid Ait-Haddou^*

^*Corresponding author for this work

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

1 Scopus citations

Abstract

We show that the weighted least squares approximation of Bézier coefficients with Hahn weights provides the best polynomial degree reduction in the Jacobi L₂-norm. A discrete analogue of this result is also provided. Applications to Jacobi and Hahn orthogonal polynomials are presented.

Original language	English
Pages (from-to)	165-176
Number of pages	12
Journal	Journal of Approximation Theory
Volume	207
DOIs	https://doi.org/10.1016/j.jat.2016.02.018
State	Published - 1 Jul 2016
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2016 Elsevier Inc.

Keywords

Bézier curves
Degree reduction
Discrete least squares
H-Bézier curves
Hahn orthogonal polynomials
Jacobi orthogonal polynomials

ASJC Scopus subject areas

Analysis
Numerical Analysis
General Mathematics
Applied Mathematics

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10.1016/j.jat.2016.02.018

Cite this

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title = "Continuous and discrete best polynomial degree reduction with Jacobi and Hahn weights",

abstract = "We show that the weighted least squares approximation of B{\'e}zier coefficients with Hahn weights provides the best polynomial degree reduction in the Jacobi L2-norm. A discrete analogue of this result is also provided. Applications to Jacobi and Hahn orthogonal polynomials are presented.",

keywords = "B{\'e}zier curves, Degree reduction, Discrete least squares, H-B{\'e}zier curves, Hahn orthogonal polynomials, Jacobi orthogonal polynomials",

author = "Rachid Ait-Haddou",

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier Inc.",

year = "2016",

month = jul,

day = "1",

doi = "10.1016/j.jat.2016.02.018",

language = "English",

volume = "207",

pages = "165--176",

journal = "Journal of Approximation Theory",

issn = "0021-9045",

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T1 - Continuous and discrete best polynomial degree reduction with Jacobi and Hahn weights

AU - Ait-Haddou, Rachid

PY - 2016/7/1

Y1 - 2016/7/1

N2 - We show that the weighted least squares approximation of Bézier coefficients with Hahn weights provides the best polynomial degree reduction in the Jacobi L2-norm. A discrete analogue of this result is also provided. Applications to Jacobi and Hahn orthogonal polynomials are presented.

AB - We show that the weighted least squares approximation of Bézier coefficients with Hahn weights provides the best polynomial degree reduction in the Jacobi L2-norm. A discrete analogue of this result is also provided. Applications to Jacobi and Hahn orthogonal polynomials are presented.

KW - Bézier curves

KW - Degree reduction

KW - Discrete least squares

KW - H-Bézier curves

KW - Hahn orthogonal polynomials

KW - Jacobi orthogonal polynomials

UR - https://www.scopus.com/pages/publications/84954258422

U2 - 10.1016/j.jat.2016.02.018

DO - 10.1016/j.jat.2016.02.018

M3 - Article

AN - SCOPUS:84954258422

SN - 0021-9045

VL - 207

SP - 165

EP - 176

JO - Journal of Approximation Theory

JF - Journal of Approximation Theory

ER -

Continuous and discrete best polynomial degree reduction with Jacobi and Hahn weights

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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Cite this