Parallel matrix factorizations on a shared memory MIMD computer

Abstract

This paper is concerned with the study of parallel algorithms for matrix factorization on a shared memory multiprocessor MIMD type computer. We consider the implementation of LU and WZ factorizations of general nonsymmetric matrices when the number of processors p is ∼O(n), where n is the order of the matrix. We show how each of these methods can be divided into noninterfering tasks which can then be executed in parallel. By studying the precedence graph of these tasks we are able to find a schedule for each algorithm which is optimum for a certain number of processors. We also consider the use of the resulting factors to solve a linear system of equations and compare the two algorithms in terms of their speedup and efficiency. It is shown that the parallel WZ algorithm attains a better efficiency using only half the processors of Doolittle's method.