Implementation of some concurrent algorithms for matrix factorization

Abstra~. Three parallel algorithms for computing the QR-factorization of a matrix are presented. The discussion is primarily concerned with implementation of these algorithms on a computer that supports tightly coupled parallel processes sharing a large common memory. The three algorithms are a Householder method based upon high-level modules, a Windowed Householder method that avoids fork-join synchronization, and a Pipelined Givens method that is a variant of the data-flow type algorithms offering large enough granularity to mask synchronization costs. Numerical experiments were conducted on the Denelcor HEP computer. The coml: rational results indicate that the Pipelined Givens method is preferred and that this is primarily due to the number of array references required by the various algorithms.