分块周期三对角矩阵逆矩阵的新算法

A new algorithm for inverse of a block period tridiagonal matrix

研究了分块周期三对角矩阵的逆问题.利用递归方法,将高阶分块周期三对角矩阵的求逆转化为低阶分块周期三对角矩阵的求逆,给出了求分块周期三对角矩阵的逆矩阵的一种新算法.通过算法的计算量的比较,新算法比直接求逆算法的计算量小.新算法的算法复杂度为4n2+O(n)次,而直接求逆的算法复杂度是5.5n2+O(n)次.算例表明新算法的计算时间短且计算精度高.

The problem of the inverse of block period tridiagonal matrices are discussed.Using the recursion method,the inversion of higher-order block period tridiagonal matrices are changed into the inversion of low-order block tridiagonal matrices,then a new algorithm for inverse of a block period tridiagonal matrix is given.Compared with the normal algorithm,the new algorithm is shorter in computation.The new algorithm has the computational complexity of 4n2＋O（n）,while the algorithm of the direct inversion has the computational complexity of 5.5n2＋O（n）.The numerical examples show that the calculation time of the new algorithm is shorter and the precision is higher.