On Gaussian quadrature formulas for the Chebyshev weight

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	On Gaussian quadrature formulas for the Chebyshev weight
	Shi, YG
	1999-05-01
发表期刊	JOURNAL OF APPROXIMATION THEORY
ISSN	0021-9045
卷号	98 期号:1 页码:183-195
摘要	This paper shows that the Chebyshev weight w(x) = (1 - x(2))(-1/2) is the only weight having the property (up to a linear transformation): For each fixed n, the solutions of the extremal problem integral(-1)(1)\Pi(k-1)(n) (x-x(k))/(m)w(x)\Pi(k=1)(n-1)(x - y(k))\(p) (1 - x(2))(p/2) w(x) dx = min(p=xn+..., Q = xn-1 +...) integral(-1)(1)\P(x)\(m)\Q(x)\(p) (1 - x(2))(p/2) w(x)dx are the same for any m, p greater than or equal to 1. (C) 1999 Academic Press.
关键词	Chebyshev weight Chebyshev polynomials Gaussian quadrature formulas
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000080011400009
出版者	ACADEMIC PRESS INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/14172
专题	中国科学院数学与系统科学研究院
通讯作者	Shi, YG
作者单位	Chinese Acad Sci, Inst Computat Math & Sci Engn Comp, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Shi, YG. On Gaussian quadrature formulas for the Chebyshev weight[J]. JOURNAL OF APPROXIMATION THEORY,1999,98(1):183-195.
APA	Shi, YG.(1999).On Gaussian quadrature formulas for the Chebyshev weight.JOURNAL OF APPROXIMATION THEORY,98(1),183-195.
MLA	Shi, YG."On Gaussian quadrature formulas for the Chebyshev weight".JOURNAL OF APPROXIMATION THEORY 98.1(1999):183-195.