26
Views
15
CrossRef citations to date
0
Altmetric
Original Articles

Explicitly preconditioned conjugate gradient method for the solution of unsymmetric linear systems

Pages 169-187 | Received 05 Sep 1991, Published online: 19 Mar 2007

References

  • Saltz , J. , Crowley , K. , Mirchandaney , R. and Berryman , H. 1990 . Run-time scheduling and execution of loops on message passing machines . J. Parall. Distr. Comput. , 8 : 739 – 747 .
  • Concus , P. , Golub , G. O. and O' Leary , D. 1976 . “ A generalized conjugate gradient method for numerical solution of elliptic partial differential equations ” . In Sparse Matrix Computations , 309 – 332 . N.Y : Academic Press .
  • Axelsson , O. 1976 . A class of iterative methods for finite element equations . Computer Meth. Appl. Mech. Engrg. , 9 : 123 – 137 .
  • Kaporin I. E. An alternative approach to estimating the iteration number of conjugate gradient method Numerical Methods and Software Kuznetsov Ju A. Academy of Science of the USSR, Department of Computational Mathematics Moscow 1990 53 72 In Russian
  • Kaporin , I. E. 1990 . On preconditioning the conjugate gradient method when solving discrete analogues of differential problems . Differents. Uravn , 26 : 1225 – 1236 . In Russian
  • Shestakov , A. I. and Anderson , D. V. 1983 . ILUCG2: Subprograms for the solution of a linear asymmetric matrix arising from a 9-point discretization . Comp. Phys. Comm. , 30 : 31 – 36 .
  • Saad , Y. 1988 . Preconditioning techniques for nonsymmetric and indefinite linear systems . J. Comp. Appl Math. , 24 : 89 – 105 .
  • George , A. and Liu , J. W. H. 1981 . Computer Solution of Large Sparse Positive Definitive Systems , Englewood Cliffs, N.J : Prentice-Hall .
  • Sinkhorn , R. 1964 . A relationship between arbitrary positive matrices and doubly stochastic matrices . Ann. Math. Statist. , 35 : 876 – 879 .
  • Marshall , A. W. and Olkin , I. 1968 . Scaling of matrices to achieve specified row and column sums . Numer. Math. , 12 : 83 – 90 .
  • Hageman , L. A. and Young , D. M. 1981 . New York : Academic Press .
  • Ortega , J. 1988 . Introduction to Parallel and Vector Solution of Linear Systems , N.Y : Plenum Press .
  • Kamath , C. and Sameh , A. 1988/1989 . A projection method for solving nonsymmetric linear systems on multiprocessors . Parallel Computing , 9 : 291 – 312 .
  • Manteuffel , T. A. 1980 . An incomplete factorization technique for positive definite systems . Math. Comput , 34 : 473 – 497 .
  • Sameh A. Bramley R. Domain Decomposition for Parallel Row Projection Algorithms Center for Supercomputing Research and Development, Univ. of Illinois Urbana, IL January 1990 CRSD Rept. No. 958
  • Saad , Y. and Schultz , M. H. 1986 . GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems . SIAM J. Sci. Statist. Comput. , 7 : 856 – 869 .
  • Sonneveld , P. 1989 . CGS, a fast Lanczos-type solver for nonsymmetric linear systems . SIAM J. Sci. Statist. Comput. , 10 : 36 – 52 .
  • Van der Vorst , H. A. 1981 . Iterative solution methods for certain sparse linear systems with a non-symmetric matrix arising from PDE-problems . J. Comput. Phys. , 44 : 1 – 19 .
  • Eisenstat , S. C. 1981 . Efficient implementation of a class of preconditioned conjugate gradient methods . SIAM J. Sci. Statist. Comput. , 2 : 1 – 4 .
  • Elman , H. C. 1989 . Relaxed and stabilized incomplete factorizations for non-self-adjoint linear systems . BIT , 29 : 890 – 915 .
  • Gustafson , J. , Montry , G. and Benner , R. 1988 . Development of parallel methods for a 1024-processor hypercube . SIAM J. Sci. Statist. Comput. , 9 : 609 – 638 .

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.