Krylov子空间E-变换GMRES(m)算法

E-transform GMRES(m) algorithm based on krylov subspace

针对GMRES(m)算法提出一种Krylov子空间E-变换GMRES(m)算法.利用单位矩阵E将GMRES(m)算法的方程组系数矩阵变换为对角矩阵,使求解问题大为简化.理论分析了算法的收敛性.通过数值实验分析,研究结果表明:在大型稀疏工程计算问题的求解中,E-变换GMRES(m)算法具有可行性、稳定性和可靠性,显著提高了GMRES(m)算法的计算精度和计算效率.

In terms of the GMRES（m） algorithm, this paper presented a E- transform GMRES （m） algorithm based on Krylov subspace. The new algorithm transforms coefficient matrix of GMRES （m） algorithm equations to a diagonal matrix by using the matrix E, which greatly simplified the solution to the problems. The convergence of this algorithm was analyzed theoretically. Through the analysis of numerical experiments, the results of study show that the E- transform GMRES （m） algorithm is feasibility, stability and reliability which improves the accuracy and efficiency of GMRES （m） algorithm significantly in large sparse engineering computing problem.