摘要
近年来,人们将正交多项式的理论推广到了σ-正交多项式．这一推广导出了具有高阶代数精度的广义高斯求积公式．本文中,我们提出一种计算σ-正交多项式零点的高效迭代方法以及计算广义高斯求积公式的科茨系数的简单方法．对于几种常用的权函数,我们还给出求积公式的若干高精度数值结果．
The theory of orthogonal polynomial has been extended recently to σ-orthogonal polynomials. These extensions lead to generalized Gaussian quadrature formulas which have high algebraic precision. In this paper an efficient iterative method based on solving the system of normal equations for computing the zeros of the σ- orthogonal polynomial is presented and a simple method for calculating the Cotes numbers of the corresponding generalized Gaussian quadrature formula is provided. Some numerical results are tabled for several commonly used weight functions.
出处
《数值计算与计算机应用》
CSCD
2006年第1期9-23,共15页
Journal on Numerical Methods and Computer Applications
基金
获国家自然科学基金(10371130)国家重点项目(2004CB318000)资助获国家自然科学基金(10571049)湖南省自然科学基金(05JJ30011)资助
关键词
σ-正交多项式
高斯求积公式
算法
σ-orthogonal polynomials, Gaussian quadrature formulas, algorithm
