三对角与五对角Toeplitz矩阵求逆的算法

An algorithm for the inverse of tri-diagonal and five-diagonal Toeplitz matrices

提出了一种求三对角与五对角Toeplitz矩阵逆的快速算法,其思想为先将Toeplitz矩阵扩展为循环矩阵,再快速求循环矩阵的逆,进而运用恰当矩阵分块求原Toeplitz矩阵的逆的算法.算法稳定性较好且复杂度较低.数值例子显示了算法的有效性和稳定性,并指出了算法的适用范围.

This paper introduces a new algorithm for the inverse of tri-diagonal and five-diagonal Toeplitz matrix.Its main idea is expanding the Toeplitz matrix to a circulant matrix first and then computing the inverse of the new circulant matrix,and finally computing the inverse of the former Toeplitz matrix with appropriate matrix spit.The algorithm has little better stability and little cost.Numerical examples illustrate the effectivity and stability of the algorithm,and indicate the scope of application of the algorithm.