基于切比雪夫节点的一类带显式系数的广义高斯求积公式

数学季刊 ›› 2011, Vol. 26 ›› Issue (2): 300-305.

基于切比雪夫节点的一类带显式系数的广义高斯求积公式

College of Mathematics and Computational Science, Shenzhen University

收稿日期:2009-01-08 出版日期:2011-06-30 发布日期:2023-05-06
作者简介:CAO Li-hua(1964-), female, native of Yantai, Shandong, an associate professor of Shenzhen University, M.S.D., engages in approximation theory; ZHAO Yi(corresponding author)(1980-), male, native of Liangshan, Shandong, a lecturer of Shenzhen University, Ph.D., engages in approximation theory.
基金资助:
Supported by the National Natural Science Foundation of China(10571121)； Supported by the Natural Science Foundation of Guangdong Province(5010509)；

Generalized Gaussian Quadrature Formulas Based on Chebyshev Nodes with Explicit Coeﬃcients

College of Mathematics and Computational Science, Shenzhen University

Received:2009-01-08 Online:2011-06-30 Published:2023-05-06
About author:CAO Li-hua(1964-), female, native of Yantai, Shandong, an associate professor of Shenzhen University, M.S.D., engages in approximation theory; ZHAO Yi(corresponding author)(1980-), male, native of Liangshan, Shandong, a lecturer of Shenzhen University, Ph.D., engages in approximation theory.
Supported by:
Supported by the National Natural Science Foundation of China(10571121)； Supported by the Natural Science Foundation of Guangdong Province(5010509)；

摘要/Abstract

摘要：

The goal here is to give a simple approach to a quadrature formula based on the divided diffierences of the integrand at the zeros of the nth Chebyshev polynomial of the first kind, and those of the (n-1)st Chebyshev polynomial of the second kind. Explicit expressions for the corresponding coefficients of the quadrature rule are also found after expansions of the divided diffierences, which was proposed in [14].

关键词: quadrature formula, expansions of divided di?erences, Chebyshev nodes

Abstract:

The goal here is to give a simple approach to a quadrature formula based on the divided diffierences of the integrand at the zeros of the nth Chebyshev polynomial of the first kind, and those of the (n-1)st Chebyshev polynomial of the second kind. Explicit expressions for the corresponding coefficients of the quadrature rule are also found after expansions of the divided diffierences, which was proposed in [14].

Key words: quadrature formula, expansions of divided di?erences, Chebyshev nodes

中图分类号:

O174.14

曹丽华, 赵毅. 基于切比雪夫节点的一类带显式系数的广义高斯求积公式[J]. 数学季刊, 2011, 26(2): 300-305.

CAO Li-hua, ZHAO Yi. Generalized Gaussian Quadrature Formulas Based on Chebyshev Nodes with Explicit Coeﬃcients[J]. Chinese Quarterly Journal of Mathematics, 2011, 26(2): 300-305.

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[2]	龚胜军, 李尚志. 三变量中的一类坐标多项式[J]. 数学季刊, 2006, 21(4): 482-487.
[3]	韩友发, 樊星, 赵岩. 状态模和两个变量的环链多项式[J]. 数学季刊, 2004, 19(4): 401-406.

基于切比雪夫节点的一类带显式系数的广义高斯求积公式

Generalized Gaussian Quadrature Formulas Based on Chebyshev Nodes with Explicit Coeﬃcients

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