论文信息 - Parallel Cholesky factorization on a shared-memory multiprocessor. Final report, 1 October 1986-30 September 1987

Parallel Cholesky factorization on a shared-memory multiprocessor. Final report, 1 October 1986-30 September 1987

A parallel algorithm is developed for Cholesky factorization on a shared-memory multiprocessor. The algorithm is based on self-scheduling of a pool of tasks. The subtasks in several variants of the basic elimination algorithm are analyzed for potential concurrency in terms of precedence relations, work profiles, and processor utilization. This analysis is supported by simulation results. The most promising variant, which the authors call column-Cholesky, is identified and implemented for the Denelcor HEP multiprocessor. Experimental results are given for this machine.

[1] Jack J. Dongarra,et al. A collection of parallel linear equations routines for the Denelcor HEP , 1984, Parallel Comput..

[2] Kai Hwang,et al. Computer architecture and parallel processing , 1984, McGraw-Hill Series in computer organization and architecture.

[3] Dianne P. O'Leary,et al. Data-flow algorithms for parallel matrix computation , 1985, CACM.

[4] J. Pasciak,et al. Computer solution of large sparse positive definite systems , 1982 .

[5] Ewing L. Lusk,et al. Implementation of monitors with macros: a programming aid for the HEP and other parallel processors , 1983 .

[6] H.F. Jordan,et al. Experience with pipelined multiple instruction streams , 1984, Proceedings of the IEEE.

[7] Franklin T. Luk,et al. Computing the Cholesky Factorization Using a Systolic Architecture , 1982 .

[8] F. Gustavson,et al. Implementing Linear Algebra Algorithms for Dense Matrices on a Vector Pipeline Machine , 1984 .

[9] Charles L. Lawson,et al. Basic Linear Algebra Subprograms for Fortran Usage , 1979, TOMS.