DGMRES Method Augmented with Eigenvectors for Computing the Drazin-inverse Solution of Singular Linear Systems  

作　　者：Bin MENG 

机构地区：[1]College of Science, Nanjing University of Aeronautics and Astronautics

出　　处：《Acta Mathematicae Applicatae Sinica》2016年第2期549-558,共10页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.11171151);Natural Science Foundation of Jiangsu Province of China(No.BK2011720)

摘　　要：The DGMRES method for solving Drazin-inverse solution of singular linear systems is generally used with restarting. But the restarting often slows down the convergence and DGMRES often stagnates. We show that adding some eigenvectors to the subspace can improve the convergence just like the method proposed by R. Morgan in [R. Morgan, A restarted GMRES method augmented with eigenvectors, SIAM J. Matrix Anal App1., 16： 1154-1171, 1995. We derive the implementation of this method and present some numerical examples to show the advantages of this method.The DGMRES method for solving Drazin-inverse solution of singular linear systems is generally used with restarting. But the restarting often slows down the convergence and DGMRES often stagnates. We show that adding some eigenvectors to the subspace can improve the convergence just like the method proposed by R. Morgan in [R. Morgan, A restarted GMRES method augmented with eigenvectors, SIAM J. Matrix Anal App1., 16： 1154-1171, 1995. We derive the implementation of this method and present some numerical examples to show the advantages of this method.

关 键 词：Drazin-inverse DGMRES Krylov subspace iterative method EIGENVECTOR 

分 类 号：O241.6[理学—计算数学]