An inversion algorithm for general tridiagonal matrix

An algorithm for the inverse of a general tridiagonal matrix is presented. For a tridiagonal matrix having the Doolittle factorization, an inversion algorithm is established. The algorithm is then generalized to deal with a general tridiagonal matrix without any restriction. Comparison with other methods is provided, indicating low computational complexity of the proposed algorithm, and its applicability to general tridiagonal matrices.     

三对角矩阵求逆的算法

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.     

一类块三对角矩阵求逆的算法

讨论了一类块三对角矩阵的求逆问题.由块三对角矩阵的LU分解,得到了其逆矩阵块元素的显式表达式.当考虑该表达式的结构特征时,可得到块元素的递推关系式,由此得到一个求逆矩阵的新算法.该算法比已有的块三对角矩阵求逆算法的计算复杂度和计算时间低.