Ring-oriented Block Matrix Factorization Algorithms for Shared and Distributed Memory Architectures

Utilizing experiences from the implementations on shared memory multiprocessors (SMM) and distributed memory multicomputers (DMM), general ring-oriented routines are developed for the LU, Cholesky, and QR factorizations. Since, all machine dependencies are comprised to a small set of communication routines, the same factorization routines can be used on both the SMM and DMM architectures. The algorithms are described on high level with focus on the porta-bility aspects. Further, detailed implementations of the LU factor-ization and machine speciic communication routines for the Alliant FX2816, Intel iPSC/2, and IBM 3090VF/600J are enclosed. Timing results show that the performance of machine speciic implementations are preserved for the general ring-oriented block algorithms.