Block GMRES Method with Inexact Breakdowns and Deflated Restarting
Block GMRES Method with Inexact Breakdowns and Deflated Restarting
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DOI：
10.1137/140961912
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发表时间：
2014-12
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影响因子：
--
通讯作者：
E. Agullo;L. Giraud;Y. Jing
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文献类型：
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作者：
E. Agullo;L. Giraud;Y. Jing
我们用块GMRES方法研究了具有多个右端的大型线性方程组的解。我们介绍了一种新的算法，它有效地处理了块Arnoldi过程产生的几乎秩亏的块的情况，并允许在重新启动时回收光谱信息。第一个特征继承了Robbe和Sadkane介绍的算法[线性代数应用，419(2006)，pp.265-285]，而第二个特征是通过扩展Morgan提出的放气重新启动策略而获得的。诺默。数学，54(2005)，第222--236页]。数值实验表明，新算法有效地结合了双亲的数值特征，并取得了较好的效果。
We consider the solution of large linear systems with multiple right-hand sides using a block GMRES approach. We introduce a new algorithm that effectively handles the situation of almost rank deficient block generated by the block Arnoldi procedure and that enables the recycling of spectral information at restart. The first feature is inherited from an algorithm introduced by Robbe and Sadkane [Linear Algebra Appl., 419 (2006), pp. 265--285], while the second one is obtained by extending the deflated restarting strategy proposed by Morgan [Appl. Numer. Math., 54 (2005), pp. 222--236]. Through numerical experiments, we show that the new algorithm combines efficiently the attractive numerical features of its two parents and outperforms them.