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

Journal of Approximation Theory

2016

Self Cite

Section: Introductionmentioning

confidence: 99%

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

Journal of Approximation Theory

2016

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“…The process of iterating formula (3.7) to express the polynomial P as a q-Bézier curve of higher degree is called degree elevation [1,15]. Denote by F N (resp.…”

Section: Q-blossom and A Generalized Hermite Identitymentioning

confidence: 99%

“…The exponential function is one of those rare functions for which the Hermite-Padé approximants can be computed explicitly, though by no means trivially. In this work, we first provide new representations of these HermitePadé approximants in terms of the blossom of the partial sums of the exponential Rachid Ait-Haddou rachid.aithaddou70@gmail.com 1 A-803 Mihogaoka 19, Ibaraki City, Osaka, 567-0047, Japan function. We then generalize these representations by expressing the Hermite-Padé approximants to the q-exponential function in terms of the q-blossom of its partial sums.…”

Section: Introductionmentioning

confidence: 99%

q-Blossoming and Hermite-Padé approximants to the q-exponential function

2016

Numer Algor

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“…This can be interpreted as projecting p ∈ P n into P m . Depending on a particular norm defined on P n , various schemes for degree reduction were derived [7,14,12,11,6,5].…”

Section: Introductionmentioning

confidence: 99%

Constrained multi-degree reduction with respect to Jacobi norms

Computer Aided Geometric Design

Bartoň

2016

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Please cite this article in press as: Ait-Haddou, R., Bartoň, M. Constrained multi-degree reduction with respect to Jacobi norms. Comput. Aided Geom. Des. (2015), http://dx.doi.org/10. 1016/j.cagd.2015.12.003 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights• We study the problem of constrained degree reduction with respect to Jacobi norms.• Our results generalize several previous findings on polynomial degree reduction.• We explore the space of Jacobi parameters on the reduced polynomial approximation.Constrained multi-degree reduction with respect to Jacobi norms AbstractWe 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 L 2 -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 L 2 -norm is presented.