Brent, Richard P2003-07-112004-05-192011-01-052004-05-192011-01-051991http://hdl.handle.net/1885/40806http://digitalcollections.anu.edu.au/handle/1885/40806This 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).166298 bytes356 bytesapplication/pdfapplication/octet-streamen-AUMIMD machinesGaussian eliminationorthogonal factorizationsingular value decompositionAmdahl's Lawparallel architecturesdata movementdata distributionlinear systemssymmetric eigenvalue problemsHestenes method1991