求三对角和周期三对角矩阵逆矩阵的一种新算法  

A New Algorithm for Computing the Inverse of Tridiagonal and Periodic Tridiagonal Matrices

作　　者：余承依[1] 陈跃辉[1] 赵立群[1] 

机构地区：[1]漳州师范学院数学与信息科学系,福建漳州363000

出　　处：《长江大学学报（自科版）（上旬）》2010年第1期126-128,共3页JOURNAL OF YANGTZE UNIVERSITY (NATURAL SCIENCE EDITION) SCI ＆ ENG

基　　金：福建省教育厅资助科技项目(JB07147);漳州师范学院科研项目(SK07008)

摘　　要：利用周期三对角矩阵的结构特点,通过适当的矩阵分块,将周期三对角矩阵的求逆转化为三对角矩阵的求逆问题,同时借助矩阵的Crout分解方法给出了一种求三对角矩阵逆矩阵的的简单算法,并将其应用到求解周期三对角矩阵逆矩阵中。数值试验表明此算法是有效的。A periodic tridiagonal matrix is transformed into a tridiagonal matrix for computing the inverse,by making the most of the structural characteristics and using the appropriate partitioned matrices. At the same time a new algorithm is proposed by crout factorization method for computing the inverse of a tridiagonal matrix,and it is applied to obtain the inverse of a periodic tridiagonal matrix. The algorithm can cut down the amount of calculation and storing capacity. From the numerical experiments it is known that the methods is effective.

关 键 词：三对角矩阵 周期三对角矩阵 逆矩阵 

分 类 号：O241.6[理学—计算数学]