三对角矩阵求逆的算法

Algorithm for the Inverse of a General Tridiagonai Matrix

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.

An algorithm for the inverse of a general tridiagonal matrix is presented. First, for the tridiagonal matrix having Doolittle factorization, an algorithm for the inverse was established. Then the algorithm was generalized to a general tridiagonal matrix without any restrictive condition. Some comparison with other methods 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.