Parallel inverse arrowhead matrix algorithms on symmetric multiprocessor systems

摘要

In this paper we present new parallel inverse arrowhead matrix algorithms, based on the concept of sparse factorization procedures, for computing explicitly exact and approximate inverses, on symmetric multiprocessor systems. Parallel explicit preconditioned conjugate gradient type methods can be used, in conjunction with parallel approximate inverses, for the efficient solution of the sparse arrowhead linear system. The parallel implementation of the new matrix inversion algorithms is discussed and numerical results are presented. Also the parallel implementation of the dominant part of the explicit preconditioned conjugate gradient type methods is exploited.