| 用解线性方程组方法求三对角矩阵的逆 |
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| 引用本文： | 刘长河,刘世祥,汪元伦. 用解线性方程组方法求三对角矩阵的逆[J]. 北京建筑工程学院学报, 2004, 20(3): 63-66 |
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| 作者姓名： | 刘长河 刘世祥 汪元伦 |
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| 作者单位： | 基础部,北京,100044;基础部,北京,100044 |
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| 基金项目： | 北京建筑工程学院校科研和教改项目 |
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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,只需进行较少次的乘除运算.第二,节省内存.除原始数据外,只定义三个一维数组,而不需任何二维数组.数值实验表明,此算法具有较高的精度.
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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(2004)03-0063-04 |
| 修稿时间： | 2004-08-30 |
Find the Inverse Matrix of Tridiagonal Matrix by Sloving Systems of Linear Algebraic Equations |
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| Liu Changhe Liu Shixiang Wang Yuanlun. Find the Inverse Matrix of Tridiagonal Matrix by Sloving Systems of Linear Algebraic Equations[J]. Journal of Beijing Institute of Civil Engineering and Architecture, 2004, 20(3): 63-66 |
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| Authors: | Liu Changhe Liu Shixiang Wang Yuanlun |
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| Affiliation: | Liu Changhe 1 Liu Shixiang 1 Wang Yuanlun 2 |
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| Abstract: | In this paper, an algorithm for finding the inverse matrix of tridiagonal matrix by sloving 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 a few in whole calculation. 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 expeiment, our algorithm is showed has high precision. |
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| Keywords: | tridiagonal matrix system of linear algebraic equations inverse matrix |
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