Abstract: An algorithm is proposed of the preconditioned generalized conjugate residual method for solving unsymmetric linear systems on a vector multiprocessor, when A is a five, seven or nine-diagonal matrix. The convergence of this iterative method is analysed. In this algorithm the iterations number is vesified to be about the same as for the multiprocessor PGCR algorithms.The resulting preconditioned GCR method has been tested by simulating a parallel-vector computer.Numerical examples indicate that the new algorithm is very efficient, when the vector multiprocessor computation is applied.

Key words: PGCR method, unsymmetric linear system, vector multiprocessor, modified incomplete choleski decomposition