A parallel algorithm for band linear systems

摘要

The work presented in this paper focuses on parallel iterative algorithm for solving band linear systems. With suitable decomposition of coefficient matrix and using the form of the iterative formula of the BSOR serial method, a parallel algorithm on distributed-memory multi-computer is established. Then Eq. (7), (8) are provided for carrying out computation required by our parallel algorithm. Furthermore, convergence is proved when the coefficient matrix A is Hermite positive definite matrix or M-matrix, and the sufficient condition is given. According to theoretical analysis, this algorithm has the same convergent velocity as BSOR method, and has the same parallelism as BJ method. In the end, two illustrative examples implemented on HP rx2600 cluster show that our algorithm’s parallel acceleration rates and efficiency are higher.