三对角矩阵求逆的算法

基金项目: 国家自然科学基金资助项目(10771030);教育部科学技术研究资助重点项目(107098);高校博士点专项科研基金资助项目(20070614001);四川省应用基础研究资助项目(2008JY0052)

Algorithm for the Inverse of a General Tridiagonai Matrix

Automation Department, CISDI Engineering Co., Ltd., Chongqing 400013, P. R. China;
School of Applied Mathematics, University of Electronic Science and Technology of China, Chengdu 610054, P. R. China;
Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, P. R. China

摘要: 研究了一般的非奇三对角矩阵的求逆，并给出了一个求逆矩阵的简单算法．首先研究了具有Doolittle分解的三对角矩阵的求逆，得到一个求逆的算法,然后将该算法推广到一般的非奇三对角矩阵上．最后给出了该算法与其它求逆方法的比较，可以看到该算法一方面计算量低，另一方面适用于不需任何附加条件的一般的非奇三对角矩阵．
- 三对角矩阵 /
- 逆矩阵 /
- Doolittle分解
Abstract: An algorithm for the inverse of a general tridiagonal matrix is presented. First, for the tridiagonal matzix having Doolittle factorization, an algorithm for the inverse was established. Then the algorithm was generalized to a general tridiagonal matrix without aqy restrictive condition. Some comparison with other methods operations of the algorithm for the inverse was discussed in the end. It is shown that the arithmetic operations of the algorithm are low and it is applicable to a general tridiagonal matrix.
- tridiaigonal matrix /
- inverse /
- Doolittle factorization

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