Processor-efficient parallel solution of linear systems. II. The positive characteristic and singular cases

Authors:
E. Kaltofen;V. Pan
Affiliations:
Dept. of Comput. Sci., Rensselaer Polytech. Inst., Troy, NY, USA;-
Venue:
SFCS '92 Proceedings of the 33rd Annual Symposium on Foundations of Computer Science
Year:
1992

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Abstract

For pt.I see Proc. 3rd Ann. ACM Symp. Parallel Algms. Architecture, p. 180-91 (1991). The authors show that over any field, the solution set to a system of n linear equations in n unknowns can be computed in parallel with randomization simultaneously in poly-logarithmic time in n and with only as many processors as are utilized to multiply two n * n matrices. A time unit represents an arithmetic operation in the field. For singular systems the parallel timings are asymptotically as fast as those for non-singular systems, due to the avoidance of binary search in the matrix rank problem, except when the field has small positive characteristic; in that case, binary search is avoided at a somewhat higher processor count measure.