Large Sparse Matrix Linear Equations Of The Parallel Algorithm

Linear equations with large sparse coefficient matrices arise in many practical scientific and engineering problems. The work presented in this paper focuses on parallel iterative algorithms for solving such large linear systems. Here, It is to be discussed as follows:(1) With suitable decomposition of block-tridiagonal coefficient matrix and using the form of the iterative formula of the BSOR method, a parallel algorithm on distributed-memory multi-computer is established in chapter two. According to theoretical analysis, it has the same convergence as BSOR method, and the same parallelism as BJ method. Moreover, four examples have been implemented on HP rx2600 cluster, and the data verify that the numerical results of this algorithm coincide with its theoretics.(2) The more flexible two-stage iterative parallel algorithm in chapter three derives from the first one. Convergence is proved when the coefficient matrix is Hermite positive definite matrix or M-matrix. Using HP rx2600 cluster, the experiment results show that the algorithm is quite competitive with multi-splitting method. Furthermore, we employ the iterative scheme in chapter three to circulant block-tridiagonal system, and get the similar results.(3) The method in chapter three extended to block-five-diagonal linear systems, we get some convergence theorems and a comparison theorem, which discusses how the decomposition of sub-blocks influences the whole velocity. In the end, the results of numerical experiments implemented on HP rx2600 cluster indicate that the algorithm is effective.