33
Views
7
CrossRef citations to date
0
Altmetric
Original Articles

Block alternating group explicit preconditioning (blage) for a class of fourth order difference schemes

&
Pages 121-136 | Received 28 Feb 1996, Published online: 20 Mar 2007

References

  • Axelsson , O. 1985 . A survey of preconditioned iterative methods for linear systems of algebraic equations . BIT , 25 : 166 – 187 .
  • Axelsson , O. 1994 . Iterative Solution Methods , New York : Cambridge University Press .
  • Barrett , R. , Berry , M. , Chan , T. F , Demmel , J. , Donato , J. , Dongarra , J. , Eijkhout , V. , Pozo , R. , Romine , C. and Van Der Vorst , H. 1994 . Templates for the solution of linear systems: Building blocks for iterative methods SIAM ,
  • Bruaset , A. M. 1995 . A survey of preconditioned iterative methods , UK : Longman Scientific & Technical .
  • Concus , P. , Golub , G. H. and Meurant , G. 1985 . Block preconditioning for the conjugate gradient method . SIAM J. Sci. Statist, Comput , 6 : 220 – 252 .
  • Evans , D. J. 1968 . The use of preconditioning in iterative methods for solving linear equations with symmetric positive definite matrices . J.I.M.A , 4 : 293 – 314 .
  • Evans , D.J. and Yousif , W. S. 1987 . The block alternating group explicit method (BLAGE) for the solution of elliptic difference equations . Int. J. Comp. Math , 22 : 177 – 185 .
  • Evans , D.J. and A. , Hadjidimos . 1986 . Alternating group explicit (AGE) iterative methods . Int. J. Comp, Math , 19 : 309 – 326 .
  • Evans , D. J. 1994 . Preconditioned Iterative Methods , Switzerland : Gordon and Breach Science Publishers .
  • Evans , D.J. and Sahimi , M. 1989 . “ The alternating group explicit (AGE) iterative method to solve parabolic and hyperbolic partial differential equations ” . In Annual Review of Numerical Fluid Mechanics and Heat Transfer II , Edited by: Tien , C. L. and Chawla , T. C. 283 – 390 . USA : Hemisphere Pub, Co .
  • Freund , R. W. and Nachtigal , N. M. 1991 . QMR: a quasi-minimal residual method for non-Hermitian linear systems . Numer. Math , 60 : 315 – 339 .
  • Freund , R. W. and Nachtigal , N. M. 1994 . An implementation of the QMR method based on coupled two-term recurrences . SIAM, J, Sci. Statist. Comput , 15 : 313 – 337 .
  • Jain , M. K. , Jain , R. K. and Mohanty , R. K. 1989 . Fourth order difference method for elliptic equations with nonlinear first derivative terms . Numerical Methods for Partial Differential Equations , 5 : 87 – 95 .
  • Jain , M. K. 1987 . Numerical Solution of Differential Equations , New Delhi : Wiley Eastern .
  • Ma , S. and Saad , Y. 1993 . “ Block-ADI preconditioners for solving sparse nonsymmetric linear systems of equations ” . In Numerical Linear Algebra , Edited by: Reichel , L , Ruttan , A. and Varga , R. S . 165 – 178 . Walter de Gruyter .
  • Saad , Y. 1995 . Iterative Methods for Large Sparse Linear Systems , New York : PWS Publishing Co .
  • Saad , Y. 1992 . “ Highly parallel preconditioners for general sparse matrices, Technical Report ” . Minneapolis, Minnesota : Army High Performance Research Center .
  • Saad , Y. and Schultz , M. H. 1985 . GMRES, a generalised minimal residual algorithm for solving nonsymmetric linear systems . SIAM J. Sci, Statist. Comput , 1 : 856 – 869 .
  • Sonneveld , P. 1989 . CGS, a fast Lanczos-type solver for nonsymmetric linear systems . SIAM. J. Sci, Statist. Comput , 10 : 36 – 52 .
  • Starke , G. 1994 . Alternating direction implicit preconditioning for nonsymmetric systems of linear equations . SIAM J. Sci. Statist. Comput , 15 : 369 – 384 .
  • Sukon , K. S. and Evans , D. J. 1996 . Two Parameter AGE method for the solution of a tridiagonal linear system of equations . Int. J. Comp. Math , 60 : 265 – 278 .

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.