Factorization methods for the parallel solution of linear systems

Thesis/Dissertation · Wed Jan 01 04:00:00 EST 1986

OSTI ID:7019829

Romine, C H

The author examines the problems of designing and analyzing solution techniques for solving large dense linear systems on a parallel processor. He restricts attention to direct, or factorization methods, as opposed to iterative methods. In particular, he give a rigorous analysis of six variants of both Gaussian elimination and Cholesky factorization, called the ijk-forms, considered by Dongarra, Gustavson, and Karp for vector computers. He selects the best forms of each algorithm, and analyzes the speedup obtained over the serial versions. With a common data distribution for the coefficient matrix (row-interleaved storage), it was shown analytically that a variant of the kij-form is optimal on a class of parallel machines. It is conjuctured that a similar result is demonstrable for the kji-form on a matrix in column-interleaved storage. Motivated by the ijk variants of the factorization stage, the author presents and analyzes two triangular-substitution algorithms that he calls the ij and ji-forms. The ji- form with row storage is the usual column-sweep algorithm described by Kuck. While no efficient triangular-substitution algorithm was previously known for a matrix in column storage, it is shown that , with some restrictions on the parallel architecture, the ij-form with column storage is efficient in parallel.

• Research Organization: Virginia Univ., Charlottesville (USA)
• OSTI ID: 7019829
• Country of Publication: United States
• Language: English

Related Subjects

99 GENERAL AND MISCELLANEOUS
990210* -- Supercomputers-- (1987-1989)
ALGORITHMS
EQUATIONS
FACTORIZATION
GAUSSIAN PROCESSES
MATHEMATICAL LOGIC
NUMERICAL SOLUTION
PARALLEL PROCESSING
PROGRAMMING