求解含多个右端向量非对称线性方程组的自适应块拟最小残量IOM(q)算法

许多实际应用问题需要求解含多个右端向量的大型非对称线性方程组 ,通常是把原来方程组分成单独几个含一个右端向量的方程组 ,再用某种迭代法分别单个求解 ,而更加经济有效的方法是应用能同时产生几个迭代向量的块迭代法来直接求解。本文在 IOM(q)算法的基础上 ,提出一种求解此类方程组的块拟最小残量 IOM(q)算法 ,讨论了如何收缩掉已收敛的部分方程组以及如何从产生的块 Krylov序列中删除线性相关或几乎线性相关向量的自适应技术。数值试验表明 ,此新的自适应块算法比块 GMRES算法及其他相关算法具有更好的收敛行为、更少的计算量和 CPU计算时间 ,是求解此类方程组的一种更加经济有效的算法。

ADAPTIVE BLOCK QMRIOM(q) METHOD FOR SOLVING UNSYMMETRIC LINEAR SYSTEMS WITH MULTIPLE RIGHT-HAND SIDES

Many applications require the solution of large unsymmetric 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. This paper proposes a new adaptive block QMR version based on the incomplete orthogonalization method (IOM( q )) for solving large multiple unsymmetric linear systems. How to incorporate deflation to drop converged linear systems, and how to delete linearly and almost linearly dependent vectors in the underlying block Krylov sequences are discussed. Numerical experiments show that the new adaptive block method has better practical performance and less computational cost and CPU time than block GMRES and other proposed methods for the solution of systems with multiple right hand sides.