Computing orthogonal polynomials on a triangle by degree raising

被引：0

作者：

Shayne Waldron

机构：

[1] University of Auckland,Department of Mathematics

来源：

Numerical Algorithms | 2006年 / 42卷

关键词：

Bernstein–Bézier form; Hahn polynomials; Jacobi polynomials; surface smoothing; primary 33C45; 65D17; secondary 41A10;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We give an algorithm for computing orthogonal polynomials over triangular domains in Bernstein–Bézier form which uses only the operator of degree raising and its adjoint. This completely avoids the need to choose an orthogonal basis (or tight frame) for the orthogonal polynomials of a given degree, and hence the difficulties inherent in that approach. The results are valid for Jacobi polynomials on a simplex, and show the close relationship between the Bernstein form of Jacobi polynomials, Hahn polynomials and degree raising.

引用

页码：171 / 179

页数：8

共 7 条

[1] Farouki R.T.(2000)Legendre–Bernstein basis transformations J. Assoc. Comput. Mach. 119 145-160
[2] Farouki R.T.(2003)Construction of orthogonal bases for polynomials in Bernstein form on triangular and simplex domains Comput. Aided Geom. Design 20 209-230
[3] Goodman T.N.T.(2000)Good degree reduction of Bézier curves using Jacobi polynomials Comput. Math. Appl. 40 1205-1215
[4] Sauer T.(2006)On the Bernstein–Bézier form of Jacobi polynomials on a simplex J. Approx. Theory 140 86-99
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