93
Views
5
CrossRef citations to date
0
Altmetric
Original Articles

Restarted Gmres Augmented With Eigenvectors For Shifted Linear Systems * Supported by the National Natural Science Foundation of China and the Science and Technology Developing Foundation of University in Shanghai of China

, &
Pages 1037-1047 | Published online: 15 Sep 2010

  • Chapman , A. and Saad , Y. 1997 . Deflated and augment Krylov subspace techniques . Numerical Linear Algebra with Application , 41 : 43 – 66 .
  • Datta , B. and Saad , Y. 1991 . Amoldi methods for large Sylvester-like observer matrix equations, and an associated algorithm for partial spectrum assignment . Linear Algebra Appl. , : 154 – 156 . 225 – 244 .
  • Emel , J. , Burrage , K. and Pohl , B. 1996 . Restarted GMRES preconditioned by deflation . J. Compta. Appl. Math. , 69 : 303 – 318 .
  • Freund , R. W. 1993 . “ Solution of shifted linear systems by quasi-minimal residual iterations. ” . In Numerical Linear Algebra , Edited by: Reichel , L. , Ruttan , Aa. and Varga , R. S. 101 – 121 . Berlin : de Gruyter .
  • Frommer , A. and Glassner , U. 1998 . Restarted GMRES for shifted linear systems . SIAMJ. Sci. Compta. , 19 : 15 – 26 .
  • Frommer , A. , Nockel , B. , Gusken , S. , Lippert , T. and Schilling , K. 1995 . Many masses on one stroke: Economic computation of quark propagators . Internat. J. Modern Phys. C , 6 : 627 – 638 .
  • Gu , Guiding . 2002 . A seed method for solving nonsymmetric linear systems with multiple right-hand sides . Intern. J. Computer Math. , 79 : 307 – 326 .
  • Gu , Guiding and Cao , Zhihao . 2001 . A block GMRES method augmented with eigenvectors . Appl Math. Comput , 121 : 271 – 289 .
  • Gu , Guiding and Wu , Hebin . 1999 . A block EN algorithm for nonsymmnetric linear systems with multiple right-hand sides . Linear Algebra Appl. , 299 : 1 – 20 .
  • Le Calvez , C. and Molina , B. 1999 . Implicitly restarted and deflated GMRES . Numerical Algorithms , 21 : 261 – 285 .
  • Morgan , R. B. 1995 . A restarted GMRES method augmented with eigenvectors . SIAMJ. Matrix Anal. Appl , 16 : 1154 – 1171 .
  • Morgan , R. B. 2000 . Implicitly restarted GMRES and Amoldi methods for nonsymmetric systems of equations . SIAM J. Matrix Anal. Appl. , 21 : 1112 – 1135 .
  • Saad , Y. 1996 . Iterative Methods for Sparse Linear Systems , Boston : PWS Publishing Co. .
  • Saad , Y. 1997 . Analysis of augmented Krylov subspace methods . SIAM J. Matrix Anal. Appl , 18 : 435 – 449 .
  • Simoncini , V. 2000 . On the convergence of restarted Krylov subspace methods . SIAM. J. Matrix Anal Appl , 22 : 430 – 452 .
  • Simoncini , V and Gallopoulos , E. 1996 . A hybrid block GMRES method for nonsymmetric systems with multiple right-hand sides . J. Comput. Appl Math. , 66 : 457 – 469 .
  • Sweet , R. 1988 . A parallel and vector variant of the cyclic reduction algorithm . SIAMJ. Sci. Statist. Comput. , 9 : 89 – 105 .
  • Young , D. and Vona , B. 1992 . On the use of rational iterative methods for solving large sparse linear systems . Appl. Numer. Math. , 10 : 261 – 278 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.