Constrained multi-degree reduction with respect to Jacobi norms

Rachid Ait-Haddou; Michael Bartoň

doi:10.1016/j.cagd.2015.12.003

Constrained multi-degree reduction with respect to Jacobi norms

Rachid Ait-Haddou^*, Michael Bartoň

^*Corresponding author for this work

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

18 Scopus citations

Abstract

We show that a weighted least squares approximation of Bézier coefficients with factored Hahn weights provides the best constrained polynomial degree reduction with respect to the Jacobi L₂-norm. This result affords generalizations to many previous findings in the field of polynomial degree reduction. A solution method to the constrained multi-degree reduction with respect to the Jacobi L₂-norm is presented.

Original language	English
Pages (from-to)	23-30
Number of pages	8
Journal	Computer Aided Geometric Design
Volume	42
DOIs	https://doi.org/10.1016/j.cagd.2015.12.003
State	Published - Feb 2016
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2015 Elsevier B.V. All rights reserved.

Keywords

Degree reduction
Hahn orthogonal polynomials
Jacobi norm
Weighted least squares

ASJC Scopus subject areas

Modeling and Simulation
Automotive Engineering
Aerospace Engineering
Computer Graphics and Computer-Aided Design

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10.1016/j.cagd.2015.12.003

Cite this

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title = "Constrained multi-degree reduction with respect to Jacobi norms",

abstract = "We show that a weighted least squares approximation of B{\'e}zier coefficients with factored Hahn weights provides the best constrained polynomial degree reduction with respect to the Jacobi L2-norm. This result affords generalizations to many previous findings in the field of polynomial degree reduction. A solution method to the constrained multi-degree reduction with respect to the Jacobi L2-norm is presented.",

keywords = "Degree reduction, Hahn orthogonal polynomials, Jacobi norm, Weighted least squares",

author = "Rachid Ait-Haddou and Michael Barto{\v n}",

year = "2016",

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doi = "10.1016/j.cagd.2015.12.003",

language = "English",

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journal = "Computer Aided Geometric Design",

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publisher = "Elsevier B.V.",

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T1 - Constrained multi-degree reduction with respect to Jacobi norms

AU - Ait-Haddou, Rachid

AU - Bartoň, Michael

PY - 2016/2

Y1 - 2016/2

N2 - We show that a weighted least squares approximation of Bézier coefficients with factored Hahn weights provides the best constrained polynomial degree reduction with respect to the Jacobi L2-norm. This result affords generalizations to many previous findings in the field of polynomial degree reduction. A solution method to the constrained multi-degree reduction with respect to the Jacobi L2-norm is presented.

AB - We show that a weighted least squares approximation of Bézier coefficients with factored Hahn weights provides the best constrained polynomial degree reduction with respect to the Jacobi L2-norm. This result affords generalizations to many previous findings in the field of polynomial degree reduction. A solution method to the constrained multi-degree reduction with respect to the Jacobi L2-norm is presented.

KW - Degree reduction

KW - Hahn orthogonal polynomials

KW - Jacobi norm

KW - Weighted least squares

UR - https://www.scopus.com/pages/publications/84954288439

U2 - 10.1016/j.cagd.2015.12.003

DO - 10.1016/j.cagd.2015.12.003

M3 - Article

AN - SCOPUS:84954288439

SN - 0167-8396

VL - 42

SP - 23

EP - 30

JO - Computer Aided Geometric Design

JF - Computer Aided Geometric Design

ER -

Constrained multi-degree reduction with respect to Jacobi norms

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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