Iterative Methods for Dense Linear Systems on Distributed Memory Parallel Computers

Muneharu YOKOYAMA  Takaomi SHIGEHARA  Hiroshi MIZOGUCHI  Taketoshi MISHIMA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E82-A   No.3   pp.483-486
Publication Date: 1999/03/25
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Selected Papers from the 11th Workshop on Circuits and Systems in Karuizawa)
iterative methods for solving dense linear systems,  conjugate gradient method,  conjugate residual method,  parallel processing,  distributed memory parallel computers,  

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The Conjugate Residual method, one of the iterative methods for solving linear systems, is applied to the problems with a dense coefficient matrix on distributed memory parallel computers. Based on an assumption on the computation and communication times of the proposed algorithm for parallel computers, it is shown that the optimal number of processing elements is proportional to the problem size N. The validity of the prediction is confirmed through numerical experiments on Hitachi SR2201.