A parallel iterative method for solving periodical block-tridiagonal linear equations

In this paper, based upon splitting the coefficient matrix, we propose a parallel iterative algorithm for periodical block-tridiagonal linear equations on distributed-memory multi-computers, which is more general applied than presented in [Lihua Chi, Jie Liu, Xiaomei Li. An effective parallel algorithm for tridiagonal linear equations, Journal of Computer 22 (2) (1999) 218-221]. Our algorithm can be easily generalized to solve the tridiagonal systems, the block-tridiagonal, and the periodical block-tridiagonal systems. The communication only needs twice between the adjacent processors per iteration. Furthermore, analysis of convergence and error about this algorithm is given. Finally, some numerical results on HP r×2600 cluster show that practice computing is consistent with theory. The algorithm has great parallel efficiency.