93
Views
8
CrossRef citations to date
0
Altmetric
Original Articles

Block jacobi preconditioning of the conjugate gradient method on a vector processor

&
Pages 71-89 | Received 05 Sep 1991, Published online: 19 Mar 2007

References

  • Ashby , S. F. , Manteuffel , T. A. and Saylor , P. E. 1990 . A taxonomy for conjugate gradient methods . SIAM J. Numer. Anal. , 27 ( 6 ) : 1542 – 1568 .
  • Faber , V. and Manteuffel , T. A. 1984 . Necessary and sufficient conditions for the existence of a conjugate gradient method . SIAM J. Numer. Anal. , 21 ( 2 ) : 352 – 362 .
  • Fletcher , R. 1975 . “ Conjugate gradient methods for indefinite systems ” . In Symposium on Numerical Analysis , 73 – 89 . New York : Springer-Verlag .
  • Freund R. Golub G. Nachtigal N. Iterative solution of linear systems Numerical Analysis Project Computer Science Department, Stanford University November 1991 Technical Report NA-91-05
  • Freund R. Golub G. Nachtigal N. An Implementation of the Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices Part I Research Institute for Advanced Computer Science NASA Ames Research Center Nov. 1990 RIACS Technical Report 90. 45
  • Freund R. Nachtigal N. An Implementation of the Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices, Part II Research Institute for Advanced Computer Science NASA Ames Research Center Nov. 1990 RIACS Technical Report 90. 46
  • Freund R. Nachtigal N. QMR: a quasi-minimal residual method for non-Hermitian linear systems IPS, ETH-Zurich Nov. 1991 Technical Report 91-05
  • Freund R. A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems Research Institute for Advanced Computer Science NASA Ames Research Center Sept 1991 18 RIACS Technical Report 91
  • Golub , G. H. and Van Loan , C. F. 1989 . Matrix Computations , Baltimore, MD : The Johns Hopkins University Press .
  • Hestenes , M. R. and Stiefel , E. 1952 . Methods of conjugate gradients for solving linear systems . J. Res. Nat. Bur. Standards , 49 : 409 – 435 .
  • Jea , K. C. and Young , D. M. 1983 . On the simplification of generalized conjugate-gradient methods for nonsymmetrizable linear systems . Linear Algebra Appl. , 52/53 : 399 – 417 .
  • Joubert , W. D. and Young , D. M. 1987 . Necessary and sufficient conditions for the simplification of generalized conjugate gradient algorithms . Linear Algebra Appl. , 88/89 : 449 – 485 .
  • Lanczos , C. 1950 . An iteration method for the solution of the eigenvalue problem of linear differential and integral operators . J. Res. Nat. Bur. Standards , 45 : 255 – 282 .
  • Levesque , J. M. and Williamson , J. W. 1989 . A guidebook to Fortran on supercomputers , New York : Academic Press .
  • Manteuffel , T. A. 1980 . An incomplete factorization technique for positive definite linear systems . Math. Comp. , 34 : 473 – 497 .
  • Metcalf , M. 1985 . Effective Fortran 77 , New York : Academic Press .
  • Metcalf , M. 1982 . Fortran Optimization , New York : Academic Press .
  • Ortega , J. M. 1988 . Introduction to Parallel and Vector Solution of Linear Systems , New York, N.Y : Plenum Press .
  • Saad , Y. and Schultz , M. H. 1986 . GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems . SIAM J. Sci. Stat. Comput. , 7 ( 3 ) : 856 – 869 .
  • Saylor , P. E. and Smolarski , D. C. 1991 . Implementation of an adaptive algorithm for Richardson's method . Linear Algebra Appl. , 154-156 ( 3 ) : 615 – 646 .
  • Young , D. M. 1971 . Iterative Solution of Large Linear Systems , New York : Academic Press .
  • Young , D. M. and Jea , K. C. 1980 . Generalized conjugate gradient acceleration of nonsymmetrizable iterative methods . Linear Algebra Appl. , 34 : 159 – 194 .

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.