Large Banded Linear Equations Of Parallel Algorithms

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 banded coefficient matrix, a parallel iterative algorithm on distributed-memory multi-computer is established in chapter two, which is based row action method. According to theoretical analysis, it is convergent and has good convergence if the coefficient matrix is a nonsingular matrix. Moreover, examples have been implemented on HP rx2600 cluster, and the data verify that the numerical results of this algorithm coincide with its theoretics.(2) A parallel split iteration algorithm for MIMD distributivity memory cluster on solving linear coefficient matrices is established in chapter three. Convergence is proved when the coefficient matrix is Hermite positive definite matrix or M-matrix. Discussing convergence range of parameter T . In the end, examples have been implemented on HPrx2600 cluster, and the data verify that the algorithm has favorable astringency and parallelism.