多右端非对称位移方程组的GMRES种子投影方法

GMRES Method with a Seed Projection for Solving Unsymmetric Shifted Systems with Multiple Right-hand Sides

考虑用GMRES方法求解多右端非对称位移方程组(A-σjI)x(j)=b(j),1 j p。基于Smith的求解多右端方程组的种子投影思想,提出了求解上述位移方程组的GMRES种子投影方法,利用种子方程组产生的Krylov子空间来求近似解。本文给出了近似解的误差界,最后数值结果显示了该方法的有效性。

We consider using GMRES method for solving unsymmetric shifted systems with multiple right\|hand sides (A-σjI)x(j)=b(j) for 1jp. Based on the seed projection proposed by Smith(1989) for solving linear systems with multiple right\|hand sides, we propose the GMRES method with a seed projection for solving (A-σjI)x(j)=b(j). A theoretical error bound is given for the approximation obtained from a projection process onto a Krylov subspace generated from the seed system. Finally, numerical results are reported to illustrate the effectiveness of the method.