Parallel algorithms for sparse systemsof linear equations and related eigenanalysis

In this paper we present the results obtained through the use of a block iterative row-projection method of Cimmino-type aimed at the solution of consistent sparse nonsymmetric sistems of liner equation Ax=b. Two approaches corresponding to two different partitionings of the matrix A are adopted. For the first one each matrix is partitioned in four almost equal-sized blocks. The last one is obtained via a reordering of the rows of the matrix yielding an automatic partitioning and a simple lest square solution. The leftmost spectrum of the matrices is also computed. The parallel algorithm employs a modification of the reverse simultaneous interations method. Our test problems range from 250 to 3600. The speeeup obtained is up to 3.3 for the solution of the systems on a CRAY Y-MP8/432 (with 4 processors), and up to 3.7 for the calculation of the leftmost spectrum.