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Original Articles

Restarted GMRES augmented with harmonic Ritz vectors for shifted linear systems

Pages 837-849 | Received 17 Aug 2004, Published online: 25 Jan 2007

References

  • 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 . Arnoldi methods for large Sylvester-like observer matrix equations, and an associated algorithm for partial spectrum assigment . Linear Algebra and its Application , 154–156 : 225 – 244 .
  • Erhel , J. , Burrage , K. and Pohl , B. 1996 . Restarted GMRES preconditioned by deflation . Journal of Computational and Applied Mathematics , 69 : 303 – 318 .
  • Feriani , A. , Perotti , F. and Simoncini , V. 2000 . Iterative system solvers for the frequency analysis of linear mechanical systems . Computer Methods in Applied Mechanics and Engineering , 190 : 1719 – 1739 .
  • 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 . SIAM Journal on Scientific Computing , 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 . International Journal Modern Physics C , 6 : 627 – 638 .
  • Gu , G. 2002 . A seed method for solving nonsymmetric linear systems with multiple right-hand sides . International Journal of Computer Mathematics , 79 : 307 – 326 .
  • Gu , G. and Wu , H. 1999 . A block EN algorithm for nonsymmetric linear systems with multiple right-hand sides . Linear Algebra and its Application , 299 : 1 – 20 .
  • Gu , G. , Zhang , J. and Li , Z. 2003 . Restated GMRES augmented with eigenvectors for shifted linear systems . International Journal of Computer Mathematics , 80 : 1039 – 1049 .
  • 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 . SIAM Journal on Matrix Analysis and Applications , 16 : 1154 – 1171 .
  • Morgan , R. B. 2000 . Implicitly restarted GMRES and Arnoldi methods for nonsymmetric systems of equations . SIAM Journal on Matrix Analysis and Applications , 21 : 1112 – 1135 .
  • Morgan , R. B. and Zeng , M. 1998 . Harmonic projection methods for large non-symmetric eigenvalue problems . Numerical Linear Algebra and its Applications , 5 : 33 – 55 .
  • Paige , C. C. , Parlett , B. N. and van der Vorst , H. A. 1995 . Approximate solutions and eigenvalue bounds from Krylov subspaces . Numerical Linear Algebra and its Applications , 2 : 115 – 133 .
  • Saad , Y. 1996 . Iterative Methods for Sparse Linear Systems , Boston : PWS Publishing Co .
  • Saad , Y. 1997 . Analysis of augmented Krylov subspace methods . SIAM Journal on Matrix Analysis and Applications , 18 : 435 – 449 .
  • Simoncini , V. 2000 . On the convergence of restarted Krylov subspace methods . SIAM Journal on Matrix Analysis and Applications , 22 : 430 – 452 .
  • Simoncini , V. 2003 . Restarted full orthogonalization method for shifted linear systems . BIT (Numerical Mathematics) , 43 : 459 – 466 .
  • Sleijpen , G. L.G. and van der Vorst , H. A.A. 1996 . A Jacobi-Davidson iteration method for linear eigenvalue problems . SIAM Journal on Matrix Analysis and Applications , 17 : 401 – 425 .
  • Sweet , R. 1988 . A parallel and vector variant of the cyclic reduction algorithm . SIAM Journal on Scientific and Statistical Computing , 9 : 89 – 105 .

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