Abstract: A new algorithm for inversing block periodic tridiagonal matrices is obtained, using the LU and UL decomposition of block tridiagonal matrix and the special structure of its inversion, the Sheman-Morrison-Woodbury formula is used during this process. Based on this algorithm, new algorithms for inversing periodic tridiagonal matrix and symmetric periodic tridiagonal matrix are also obtained. The computing complexity and the computing time of these algorithms are lower than the traditional algorithms.

Key words: periodic tridiagonal matrix, symmetric periodic tridiagonal matrix, block periodic tridiagonal matrix, inverse matrix

摘要： 根据分块三对角矩阵逆矩阵的特殊结构，利用其LU和UL分解，并使用Sheman-Morrison-Woodbury公式，得到一个求分块周期三对角矩阵逆矩阵的新算法，并由该算法得到求周期三对角矩阵和对称周期三对角矩阵逆矩阵的新算法。新算法比传统算法的计算复杂度和计算时间要低。

关键词: 周期三对角矩阵, 对称周期三对角矩阵, 分块周期三对角矩阵, 逆矩阵