Design of Optimal Array Processors for Two-Step Division-Free Gaussian Elimination

Shietung PENG  Stanislav G. SEDUKHIN  

IEICE TRANSACTIONS on Information and Systems   Vol.E82-D   No.12   pp.1503-1511
Publication Date: 1999/12/25
Online ISSN: 
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Algorithm and Computational Complexity
linear system,  parallel algorithm,  parallel architecture,  systolic array processors,  

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The design of array processors for solving linear systems using two-step division-free Gaussian elimination method is considered. The two-step method can be used to improve the systems based on the one-step method in terms of numerical stability as well as the requirements for high-precision. In spite of the rather complicated computations needed at each iteration of the two-step method, we develop an innovative parallel algorithm whose data dependency graph meets the requirements for regularity and locality. Then we derive two-dimensional array processors by adopting a systematic approach to investigate the set of all admissible solutions and obtain the optimal array processors under linear time-space scheduling. The array processors is optimal in terms of the number of processing elements used.