| 关于Gauss-Turán求积公式的注记 |
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| 引用本文： | 杨士俊,王兴华. 关于Gauss-Turán求积公式的注记[J]. 计算数学, 2003, 25(2): 199-208 |
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| 作者姓名： | 杨士俊 王兴华 |
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| 作者单位： | 1. 浙江大学数学与信息科学系,杭州,310028;杭州师范学院数学系,杭州,310012
2. 浙江大学数学与信息科学系,杭州,310028;温州大学数学与信息科学学院,温州,325200 |
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| 基金项目： | 国家重点基础研究专项经费(批准号19990328)，浙江省自然科学基金(批准号100002)资助项目. |
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| 摘 要： | 1.引言 设w(x)是区间[-1,1]上的权函数,N是自然数集,X1,…,Xn(n∈N)是对应于权函数w(x)的n次正交多项式的零点,则具有最高代数精度2n-1,其中Πn表示所有次数≤n的多项式空间. 1950年,Turan[1]将上述经典的Gauss求积公式予以推广,证明了,若
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| 关 键 词： | Gauss-Turán求积公式 Hermite插值多项式 s-正交多项式 Cotes数 最高代数精度 |
| 修稿时间： | 2001-04-11 |
REMARKS ON SOME GAUSS-TURAN QUADRATURES |
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| Yang Shijun. REMARKS ON SOME GAUSS-TURAN QUADRATURES[J]. Mathematica Numerica Sinica, 2003, 25(2): 199-208 |
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| Authors: | Yang Shijun |
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| Affiliation: | Yang Shijun (Department of Mathematics and Information Sciences, Zhejiang University,Hangzhou, 310028; Department of Mathematics, Hangzhou Normal College, Hangzhou, 310012)Wang Xinghua (Department of Mathematics and Information Sciences, Zhejiang University,Hangzhou, 310028;College of Mathematics and Information Sciences, Wenzhou University, Wenzhou, 325200,Zhejiang Province) |
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| Abstract: | Ying Guang Shi(1995 & 1999) obtained some; quadratures, which is based on the zeros of the so-called s-orthogonal polynomials with respect to some Jacobi weights,of highest algebraic degree of precision of Gauss-Turan type. Following B.Bojanov(1996) and our recent work, we give here a simple and unified approach to these questions of this type and obtain quadratures in terms of the divided differences, which is based on an appropriate representation of the Hermite interpolating polynomial, of corresponding function at the zeros of the appropriate s-orthogonal polynomial with multiplicities. |
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| Keywords: | Gauss-Turan quadrature Hermite interpolating polynomial s-orthogonal polynomial Cotes number highest algebraic degree of precision |
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