A judiciously chosen symmetric permutation can significantly reduce the amount of storage and computation for the Cholesky factorization of sparse matrices. On distributed memory machines, the issue of mapping data and computation on processors is also important. Previous research on ordering for parallelism has focussed on idealized measures like ezecution time on an unbounded number of processors, with zero communication costs. In this paper, we propose an ordering and mapping algorithm that attempts to minimize communication and performs load-balancing of work among the processors. Performance results on an Intel iPSC/860 hypercube are presented to demonstrate its effectiveness.

No abstract

No abstract

No abstract

Abstrslct -The concepi of supernodes has been widely used in the design of algorithms or the solurion of sparse linear systems of equations. his paper discusses the use of supernodes in (he design of algorithms for s wse Cholesky facroriralion on distriburod-memory mu&-cessors. A new algorithm that is communicarion eflcient, hus good load bulunce, and benefrls signifrcanrly from supernodes is presented. A taronomy of dislribured s arse Cholesb faclorizalbn algorithm is proposed. &rformance results on an Inre1 ffSCiS60 rndtiproerrsor are reporled.