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Original Articles

Iterative methods for solving sparse linear systems with a parallel preconditioner

Pages 111-119 | Received 17 Jun 1991, Published online: 19 Mar 2007

References

  • Anderson , E. C. 1988 . “ Parallel implementation of preconditioned conjugate gradient methods for solving sparse systems of linear equations ” . In Technical Report 805, CSRD , Urbana, IL : University of Illinois .
  • Anderson E. C. Saad Y. Solving sparse triangular systems on parallel computers Technical Report 794, CSRD University of Illinois Urbana, IL 1988
  • 1990 CF77 Compiling system, vol. 4 Parallel Processing Guide, Cray Research Inc., SG-3074 4. 0,
  • Eisenstat , S. C. , Elman , H. C. and Schultz , M. H. 1983 . Variational iterative methods for nonsymmetric systems of linear equations . SIAM J. Numer, Anal. , 20 : 345 – 357 .
  • Hestenes , M. R. and Stiefel , E. 1952 . Methods of conjugate gradients for solving linear systems . Nat. Bureau Stand. J. Res. , 49 : 409 – 436 .
  • Gambolati , G. , Pini , G. and Zilli , G. 1988 . Numerical comparisons of preconditionings for large sparse finite element problems . Numer. Meth. for Partial Diff. Eqns , 4 : 139 – 157 .
  • Meijerink , J. A. and Van der Vorst , H. A. 1977 . An iterative solution method for linear systems of which the coefficient matrix is a symmetric . M-matrix, Math, Comp. , 31 : 148 – 162 .
  • Nagel , W. E. 1990 . Exploiting Autotasking on a CRAY Y-MP: an improved software interface to multitasking . Parallel Computing , 13 : 225 – 233 .
  • Oppe T. C. Joubert W. D. Kinkaid D. R. University of Texas at Austin 1988 NSPCG User's guide. A package for solving large linear systems by various iterative methods. Technical Report
  • Pini , G. and Zilli , G. 1989 . Preconditioned iterative algorithms for large sparse unsymmetric problems . Numer. Meth. for Partial Diff. Eqns , 5 : 107 – 120 .
  • Pini , G. and Gambolati , G. 1990 . Is a simple diagonal scaling the best preconditioner for conjugate gradients on supercomputers? . Adv. Water Resources , 3 : 147 – 147 . 153
  • Pini , G. and Zilli , G. 1990 . On vectorizing the preconditioned generalized conjugate residual methods . Intern. J. Computer. Math. , 33 : 195 – 207 .
  • Saad , Y. and Schultz , M. H. 1985 . Conjugate gradient-like algorithms for solving nonsymmetric linear systems . Math. Comput. , 44 : 417 – 424 .
  • Saad , Y. 1989 . Krylov subspace methods on supercomputers . Siam J. Sci. Stat. Comput. , 10 : 1200 – 1232 .
  • Van der Vorst , H. A. 1989 . High performance preconditioning . Siam J. Sci. Stat. Comput. , 10 : 1174 – 1185 .
  • Wing , O. and Huang , J. W. 1980 . A computational model of parallel solution of linear equations . IEEE Transactions on Computers , C 29 : 632 – 638 .

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