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A note on constrained degree reduction of polynomials in Bernstein–Bézier form over simplex domain

✍ Scribed by Lizheng Lu

Publisher: Elsevier Science
Year: 2009
Tongue: English
Weight: 273 KB
Volume: 229
Category: Article
ISSN: 0377-0427
DOI: 10.1016/j.cam.2008.10.032

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✦ Synopsis

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-Bézier 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.

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Constrained degree reduction of polynomials in Bernstein–Bézier form over simplex domain

✍ Hoi Sub Kim; Young Joon Ahn 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 145 KB

In this paper we show that the orthogonal complement of a subspace in the polynomial space of degree n over d-dimensional simplex domain with respect to the L 2 -inner product and the weighted Euclidean inner product of BB (Bézier-Bernstein) coefficients are equal. Using it we also prove that the be