多右端项对称线性方程组的Lanczos种子投影方法

摘要

求解多右端项位移线性方程组的迭代方法中,GMRES种子投影方法是一个有效方法, 但是当系数矩阵为对称矩阵时,该方法的有效性往往会降低. 为解决这一问题,提出求解对称多右端项位移方程组的Lanczos种子投影方法,分析算法的残量性质并做了数值实验. 数值实验结果表明,新算法对求解对称多右端项位移方程组是有效的.%Seed projection methods for solving multiple right-hand sides system was studied in this paper. Generally,GMRES seed projection method was one effectual method for solving multiple right-hand sides system,but when the coefficient matrix was symmetric,effects of the method would be worse. Lanczos seed projection methods for solving symmetric system with multiple right-hand sides were proposed in this paper,and the residual estimation were analyzed. The numerical results showed the method was the effective.