非对称线性方程组的块广义最小向后误差算法

许多科学领域都需要求多个右边值的大型非对称线性方程组，使用块方法同时计算所有的方程组比分别计算每一个方程要有效得多。因此，能同时计算所有方程的块迭代方法比单独计算每一个方程的迭代法要有效得多。本提出了一个块GMBACK方法求解有多个右边值的大型非对称线性方程组，该方法利用块Arnoldi过程构造Krylov子空间来求解Xm∈X0 Km(A,R0)使得矩阵A的扰动范数最小。

A BLOCK GENERALIZED MINIMUM BACKWARD (BGMBACK) ERROR ALGORITHM FOR NONSYMMETRIC LINEAR SYSTEMS

Many applications require the solution of large nonsymmetric linear systems with multiple right-hand sides. Instead of applying an iterative method to each of these systems individually, it is often more efficient to use a block version of the method that generates iterates for all the systems simultaneously. In this paper, we propose a block version of generalized minimum backward (GMBACK) for solving large multiple nonsymmetric linear systems. The new method employs the block Arnoldi process to construct a basis for the Krylov subspace Km(A, R0) and seeks Xm∈X0+Km(A, R0) to minimize the norm of the perturbation to the data given in A.