65
Views
4
CrossRef citations to date
0
Altmetric
Miscellany

Multiple search direction conjugate gradient method II: theory and numerical experiments

, , &
Pages 1289-1307 | Accepted 10 Mar 2004, Published online: 25 Jan 2007

References

References

  • Axelsson , O and Vassilevski , PS . (1991) . A black box generalized conjugate gradient solver with inner iterations and variable-step preconditioning . SIAM J. Matrix Anal. Appl. , 12 : 625 – 644 .
  • Basermann , A . (1997) . Conjugate gradient and Lanczos methods for sparse matrices on distributed memory multiprocessors . J. Parallel Distr. Comput. , 45 : 46 – 52 .
  • Basermann , A , Reichel , B and Schelthoff , C . (1997) . Preconditioned CG methods for sparse matrices on massively parallel machines . Parallel Comput. , 23 : 381 – 398 .
  • Chronopoulos , AT and Gear , CW . (1989) . s-Step iterative methods for symmetric linear systems . J. Comp. Appl. Math. , 25 : 153 – 168 .
  • Crone , L and van der Vorst , HA . (1993) . Communication aspects of the conjugate gradient method on distributed-memory machines . Supercomputer , X ( 6 ) : 4 – 9 .
  • D'Azevedo EF Romine C (1993) LAPACK working note 56: reducing communication costs in the conjugate gradient algorithm on distributed memory multiprocessors Technical Reports. Computer Science Department, University of Knoxville Knoxville TN
  • da Sturler , E . (1996) . A performance model for Krylov subspace methods on mesh-based parallel computers . Parallel Comput. , 22 : 57 – 74 .
  • Demmel JW Health MT van der Vorst HA (1993) Parallel Numerical Linear Algebra In Acta Numerica 1993. Cambridge University Press Cambridge
  • Field , MR . (1998) . Optimizing a parallel conjugate gradient solver . SIAM J. Sci. Comput. , 19 : 27 – 37 .
  • Gu T-X Liu X-P Mo Z-Y Chi X-B (in press) Multiple search direction conjugate gradient method I: Methods and their propositions Int. J. Comput. Math.
  • Hesrenses , MR and Stiefel , E . (1952) . Method of conjugate gradients for solving linear systems . J. Res. Nat. Bur. Stand. , 49 : 409 – 436 .
  • Meurant , G . (1984) . The block preconditioned conjugate gradient method on vector computers . BIT , 24 : 623 – 633 .
  • Meurant , G . (1987) . Multitasking the conjugate gradient method on the CRAY X-MP/48 . Parallel Comput. , 5 : 267 – 280 .
  • O'Leary , DP . (1980) . The block conjugate gradient algorithm and related methods . Lin. Alg. Appl. , 29 : 293 – 322 .
  • Radicati di Brozolo , G and Robert , Y . (1989) . Parallel conjugate gradient-like algorithms for solving sparse non-symmetric systems on a vector multiprocessor . Parallel Comput. , 11 : 223 – 329 .
  • Reid JK (1971) On the method of conjugate gradients for the solution of large sparse systems of linear equation In: J. K. Reid (Ed.) Large Sparse Sets of Linear Equations, Academic Press pp. 231–254
  • Saad , Y . (1981) . Krylov subspace methods for solving large unsymmetric linear systems . Math. Comput. , 155 : 105 – 126 .
  • Saad , Y . (1989) . Krylov subspace methods on supercomputers . SIAM J. Sci. Comput. , 10 : 1200 – 1232 .
  • Saad Y (1996) Iterative Methods for Sparse Linear Systems, PWS Publishing Company Boston
  • Tang , WP . (1992) . Generalized Schwarz splittings . SIAM J. Sci. Stat. Comput. , 13 : 573 – 595 .
  • Jinchao Xu . (1992) . Iterative methods by space decomposition and subspace correction . SIAM Rev. , 34 ( 4 ) : 581 – 613 .
  • Young DM (1971) Iterative Solution of Large Linear Systems, Academic Press NY

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.