周期三对角矩阵求逆的快速算法  

Fast Inversion of Periodic Tridiagonal Matrices

作　　者：唐达[1] 

机构地区：[1]上海电机学院数理教学部,上海201306

出　　处：《上海电机学院学报》2013年第5期300-304,共5页Journal of Shanghai Dianji University

摘　　要：利用t向量来求周期三对角矩阵之逆。求逆的运算量为2n2+O(n)乘除法及n2+O(n)加减法。该算法计算量小且计算精度高。若对t向量进行截断、快速求逆,则求逆的计算量仅与n成正比。与现有快速算法相比,清除了电脑内存溢出的情况。文末列出了部分数值算例。In this paper, inversion of periodic tridiagonal matrices is discussed using the tvec- tot. Computational complexity of the inversion is 2n2 2r-O（n） of multiplication and division and n2 4-O（n） of addition and subtraction. The algorithm has a low computational cost as well as high precision. The computational cost is further reduced to become proportional to n if the t vector is truncated and fast inverse＆ In contrast to the existing fast algorithms, the out-of-memory errors no longer occur. Numerical examples are presented.

关 键 词：周期三对角矩阵 逆矩阵 溢出 t向量 快速求逆 

分 类 号：O241.6[理学—计算数学]