Orthogonal polynomials and Gaussian quadrature for refinable weight functions

被引：8
|
作者：
Laurie, DP [1 ]
de Villiers, JM [1 ]
机构：
[1] Univ Stellenbosch, Dept Math, ZA-7602 Matieland, South Africa
来源：
APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS | 2004年 / 17卷 / 03期
关键词：
refinable function; orthogonal polynomials; Gaussian quadrature; modified moments; Legendre series;
D O I：
10.1016/j.acha.2004.06.002
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We show how to compute the modified moments of a refinable weight function directly from its mask in O(N(2)n) rational operations, where N is the desired number of moments and n the length of the mask. Three immediate applications of such moments are: . the expansion of a refinable weight function as a Legendre series; . the generation of the polynomials orthogonal with respect to a refinable weight function; . the calculation of Gaussian quadrature formulas for refinable weight functions. In the first two cases, all operations are rational and can in principle be performed exactly. (C) 2004 Published by Elsevier Inc.
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页码：241 / 258
页数：18
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