Implementation of some concurrent algorithms for matrix factorization

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 computational 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. © 1986.