Construction of sigma-orthogonal polynomials and gaussian quadrature formulas

doi:10.1007/s10444-007-9033-8

CSpace

	Construction of sigma-orthogonal polynomials and gaussian quadrature formulas
	Shi, Ying Guang ; Xu, Guoliang
	2007-07-01
发表期刊	ADVANCES IN COMPUTATIONAL MATHEMATICS
ISSN	1019-7168
卷号	27 期号:1 页码:79-94
摘要	Let d alpha be a measure on R and let sigma = (m(1), m(2),..., m(n)), where m(k) >= 1, k = 1, 2,..., n, are arbitrary real numbers. A polynomial omega(n)(x) := (x - x(1))(x - x(2))...(x-x(n)) with x(1) <= x(2) <=... <= x(n) is said to be the nth sigma-orthogonal polynomial with respect to da if the vector of zeros (x(1), x(2),..., x(n))(T) is a solution of the extremal problem integral(R)Pi(n)(k=1)\|x-x(k)\|(mk)d alpha(x)=min(y1 <= y2 <=...<= yn)integral(R)Pi(n)(k=1)\|x-y(k)\|(mk)d alpha(x). In this paper the existence, uniqueness, characterizations, and continuity with respect to sigma of a sigma-orthogonal polynomial under a more mild assumption are established. An efficient iterative method based on solving the system of normal equations for constructing a sigma-orthogonal polynomial is presented when all the m(k) are arbitrary real numbers no less than 2. A simple method to calculate the Cotes numbers of the corresponding generalized Gaussian quadrature formula when all the m(k) are positive integers no less than 2 is provided. Finally, some numerical examples are also given.
关键词	sigma-orthogonal polynomials existence uniqueness characterizations continuity Gaussian quadrature formulas algorithm
DOI	10.1007/s10444-007-9033-8
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000247383500004
出版者	SPRINGER
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/5048
专题	中国科学院数学与系统科学研究院
作者单位	1.Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R China 2.Hunan Normal Univ, Dept Math, Changsha, Hunan, Peoples R China 3.Chinese Acad Sci, LSEC, Inst Computat Math, Acad Math & Syst Scia, Beijing, Peoples R China
推荐引用方式 GB/T 7714	Shi, Ying Guang,Xu, Guoliang. Construction of sigma-orthogonal polynomials and gaussian quadrature formulas[J]. ADVANCES IN COMPUTATIONAL MATHEMATICS,2007,27(1):79-94.
APA	Shi, Ying Guang,&Xu, Guoliang.(2007).Construction of sigma-orthogonal polynomials and gaussian quadrature formulas.ADVANCES IN COMPUTATIONAL MATHEMATICS,27(1),79-94.
MLA	Shi, Ying Guang,et al."Construction of sigma-orthogonal polynomials and gaussian quadrature formulas".ADVANCES IN COMPUTATIONAL MATHEMATICS 27.1(2007):79-94.