The Improved Quasi-Minimal Residual Method on Massively Parallel Distributed Memory Computers

概要

論文の詳細を見る
For the solutions of linear systems of equations with unsymmetric coefficient matrices, we propose an improved version of the quasi-minimal residual (IQMR) method by using the Lanczos process as a major component combining elements of numerical stability and parallel algorithm design. For Lanczos process, stability is obtained by a coupled two-term procedure that generates Lanczos vectors scaled to unit length. The algorithm is derived such that all inner products and matrix-vector multiplications of a single iteration step are independent and communication time required for inner product can be over-lapped efficiently with computation time. Therefore, the cost of global communication on parallel distributed memory computers can be significantly reduced. The resulting IQMR algorithm maintains the favorable properties of the Lanczos process while not increasing computational costs. The efficiency of this method is demonstrated by numerical experimental results carried out on a massively parallel distributed memory computer, the Parsytec GC/PowerPlus.
社団法人電子情報通信学会の論文
1997-09-25