A New Algorithm for Solving Periodic Tridiagonal Systems

摘要

Based on a modified LU factorization of a periodic tridiagonal matrix, a new modified algorithm for solving periodic tridiagonal systems is presented by using the Sherman-Morrison formula in this paper. The algorithm has less computational cost than the Thomas algorithm for solving periodic tridiagonal systems. Moreover, two parameters are included and parallel computations can be implemented in the algorithm. The feasibility and stability of the algorithms are analyzed. Numerical examples illustrate the effectiveness of the algorithm.