Parallel algorithms in linear algebra

Details Parallel algorithms in linear algebra Parallel algorithms in linear algebra

2010-04-30

arxiv.org/abs/1004.5437v1

Algorithms and Architectures: Proceedings of the Second NEC Research Symposium (edited by T. Ishiguro), SIAM, Philadelphia, 19

Computer Science

Data Structures and Algorithms

17 pages. An old Technical Report, submitted for archival purposes. For further details see http://wwwmaths.anu.edu.au/~brent/

Scientific paper

This report 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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