The pgcr method for solving unsymmetric linear systems on a vector multiprocessor

Abstract

In this paper the algorithm of the preconditioned generalized conjugate residual method for solving unsymmetric linear systems on a vector multiprocessor are proposed, when A is five, seven or nine-diagonal matrix. The convergence of these iterative methods is analysed. We show that for this algorithm the number of iterations is about the same as for the multiprocessor PGCR algorithms. The resulting preconditioning GCR method has been tested on simulation parallel-vector computer. Numerical examples indicate that the new algorithm is very efficient, since the vector multiprocessor computation can be applied.

Keywords:

• PGCR method
• unsymmetric linear system
• vector multiprocessor
• modified incomplete Choleski decomposition

Subject Classification C.R Categories:

• G.1.3
• F.1.2
• C.1.2

AMS(MOS):

• 65F10
• 65F15

^*This work was supported in part by the Natural Science Foundation of China and CAEP.

^*This work was supported in part by the Natural Science Foundation of China and CAEP.

Notes

^*This work was supported in part by the Natural Science Foundation of China and CAEP.