求解线性方程组的加权GMRES-DR算法

A Weighted GMRES-DR Algorithm for the Linear System of Equations

摘要

摘要:在分析GMRES-DR的基础上,将加权技术和GMRES-DR算法结合,从而加快GMRES-DR算法的收敛速度,并从理论上证明了加权GMRES-DR算法的每次循环生成仍是Krylov子空间,此外数值试验验证了该算法的有效性.

Abstract:The GMRES-DR method is an efficient iterative method for the solution of equation sets with large-scale sparse non-symmetric matrix. Based on the analysis of GMRES-DR, in combination with the weighted technology, the velocity of convergence of the GMRES-DR algorithm is accelerated, and it is proven theoretically that the circulatory generations each time of the weighted GMRES-DR algorithm are still Krylov sub-spaces and the numerical experimentation proves the validity of the said algorithm.