A note on constrained degree reduction of polynomials in Bernstein-Bezier form over simplex domain

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:229

Article

Lu, Lizheng¹ 

[1] Zhejiang Gongshang Univ, Coll Stat & Math, Hangzhou 310018, Peoples R China

关键词: Simplex domain;    Bernstein polynomials;    Constrained degree reduction;    Degree elevation;   

DOI  :  10.1016/j.cam.2008.10.032

来源: Elsevier

【 摘 要 】

In the paper [H.S. Kim, Y.J. Ahn, Constrained degree reduction of polynomials in Bernstein-Bezier form over simplex domain, J. Comput. Appl. Math. 216 (2008) 14-19], Kim and Ahn proved that the best constrained degree reduction of a polynomial over d-dimensional simplex domain in L-2-norm equals the best approximation of weighted Euclidean norm of the Bernstein-Bezier coefficients of the given polynomial. In this paper, we presented a counterexample to show that the approximating polynomial of lower degree to a polynomial is virtually non-existent when d >= 2. Furthermore, we provide an assumption to guarantee the existence of solution for the constrained degree reduction. (C) 2008 Elsevier B.V. All rights reserved.

【 授权许可】

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