PARALLEL IMPLEMENTATION OF A ROW-PROJECTION METHOD FOR SOLVING SPARSELINEAR-SYSTEMS

In this paper we present the results obtained through the use of an ac celerated block iterative row-projection method of Cimmino-type aimed at the solution of consistent sparse nonsymmetric systems of linear eq uations. Two approaches corresponding to two different partitionings o f the matrix A are adopted. For the first one each matrix is partition ed into four almost equal-sized blocks. The sparse least squares subpr oblems are then solved concurrently with an iterative Lanczos algorith m. We propose a second partitioning obtained via a reordering or the r ows of the matrix yielding an automatic partitioning and a simple leas t squares solution. The test problems are unstructured sparse nonsymme tric matrices ranging in dimension from 500 to 2000. The speedup obtai ned is up to 3.2 on a Cray Y-MP8/432 (with 4 processors).