| 一类反对称迭代矩阵半迭代法的收敛性 |
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| 引用本文： | 曹晓春,畅大为.一类反对称迭代矩阵半迭代法的收敛性[J].江西师范大学学报(自然科学版),2007,31(2):189-192. |
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| 作者姓名： | 曹晓春 畅大为 |
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| 作者单位： | 陕西师范大学,数学与信息科学学院,陕西,西安,710062 |
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| 摘 要： | 半迭代法或称Chebyshev半迭代法是解线性方程组的一个常用且比较有效的方法,它大大提高了矩阵的收敛速度.本文依据Varga,Young,胡家赣书中介绍的迭代矩阵为对称阵时,半迭代法的收敛性的理论,以Chebyshev多项式及其基本性质作为基本工具,对一类反对称迭代矩阵,研究其半迭代法的收敛情况.从而为扩大半迭代法的适用范围奠定了基础.
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| 关 键 词： | 反对称迭代矩阵 半迭代法 Chebyshev多项式 谱半径 收敛 |
| 文章编号： | 1000-5862（2007）02-0189-04 |
| 修稿时间： | 2006-09-20 |
Convergence of Semi-Iterative Method for a Class of Antisymmetric Iterative Matrix |
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| CAO Xiao-chun,CHANG Da-wei.Convergence of Semi-Iterative Method for a Class of Antisymmetric Iterative Matrix[J].Journal of Jiangxi Normal University (Natural Sciences Edition),2007,31(2):189-192. |
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| Authors: | CAO Xiao-chun CHANG Da-wei |
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| Abstract: | Semi-iterative Method is a normal and effective method of solving the linear algebra equation.It can often achieve a large improvement of the convergence.Convergence of semi-iterative method was discussed by Varga,Young and HU Jia-gan when iterative matrix is symmetric.In this paper,using Chebyshev polynomial and its properties,we obtain the convergence of semi-iterative method for a class of antisymmetric iterative matrix.Thus we extend the usual convergence condition to a new situation. |
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| Keywords: | antisymmetric iterative matrix semi-iterative method Chebyshev polynomial spectral radius convergence |
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