| 用解线性方程组方法求三对角矩阵的逆及其应用 |
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| 引用本文： | 刘长河,汪元伦,刘世祥. 用解线性方程组方法求三对角矩阵的逆及其应用[J]. 北京建筑工程学院学报, 2005, 21(3): 59-62,70 |
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| 作者姓名： | 刘长河 汪元伦 刘世祥 |
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| 作者单位： | 1. 北京建筑工程学院,基础部,北京,100044
2. 绵阳师范学院,数学与信息科学系,四川绵阳,621000 |
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| 摘 要： | 根据三对角矩阵的特点,给出一种利用解线性方程组的方法求三对角矩阵的逆矩阵的算法.该算法有两个优点.第一,运算量小. 在整个计算过程中,只需进行O(3/2n2)次乘除运算.第二,节省内存. 除原始数据外,只定义3个一维数组,而不需任何二维数组.数值实验表明,它具有较高的精度.此算法特别适用于求解一大批具有相同的系数矩阵,而具有各自不同的非齐次项的线性代数方程组.
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| 关 键 词： | 三对角矩阵 线性方程组 逆矩阵 |
| 文章编号： | 1004-6011（2005）03-0059-04 |
| 收稿时间： | 2005-06-03 |
| 修稿时间： | 2005-06-03 |
Find the Inverse Matrix of Tridiagonal Matrix by Solving Systems of Linear Algebraic Equations |
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| Liu Changhe,Wang Yuanlun,Liu Shixiang. Find the Inverse Matrix of Tridiagonal Matrix by Solving Systems of Linear Algebraic Equations[J]. Journal of Beijing Institute of Civil Engineering and Architecture, 2005, 21(3): 59-62,70 |
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| Authors: | Liu Changhe Wang Yuanlun Liu Shixiang |
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| Affiliation: | 1.Dept. of Basic Sciences, Beijing, 100044; 2. Dept. of Information and Mathematics, Mianyang Normal College, Mianyan, 621000 |
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| Abstract: | In this paper,an algorithm for finding the inverse matrix of tridiagonal matrix by solving systems of linear algebraic equations is proposed.This algorithm is got according to the peculiarity of tridiagonal matrix.Our algorithm has two advantages.First,the amount of arithmetic operation is small.The number of multiplication and division operations is only about O3[]2n~2[JB>2)].Second,memory units of computer are saved.Only three one-dimension arrays are defined during the course of calculation,while no two-dimension arrays are needed.By valuation experiment,our algorithm is showed has high precision.This algorithm is particularly suitable for solving a lot of systems of linear algebra equations,which have the same coefficient matrix and different non-homogeneous items. |
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| Keywords: | tridiagonal matrix system of linear algebraic equations inverse matrix |
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