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

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