Parallel algorithms in linear algebra

128. R. P. Brent, Parallel algorithms in linear algebra, Algorithms and Architectures: Proceedings of the Second NEC Research Symposium held at Tsukuba, Japan, August 1991 (edited by T. Ishiguro), SIAM, Philadelphia, 1993, 54-72. Also Technical Report TR-CS-91-06, Computer Sciences Laboratory, ANU, August 1991, 17 pp. arXiv:1004.5437v1

Abstract: dvi (2K), pdf (59K), ps (25K).

Technical Report: dvi (30K), pdf (149K), ps (78K).

Transparencies: pdf (94K), ps (52K).


This paper provides an introduction to algorithms for fundamental linear algebra problems on various parallel computer architectures, with the emphasis on distributed-memory MIMD machines.

To illustrate the basic concepts and key issues, we consider the problem of parallel solution of a nonsingular linear system by Gaussian elimination with partial pivoting. This problem has come to be regarded as a benchmark for the performance of parallel machines. We consider its appropriateness as a benchmark, its communication requirements, and schemes for data distribution to facilitate communication and load balancing.

In addition, we describe some parallel algorithms for orthogonal (QR) factorization and the singular value decomposition (SVD).

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