38
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

An efficient variant of gauss-jordan type algorithms for direct and parallel solution of dense linear systems

&
Pages 387-410 | Received 20 Aug 1999, Published online: 19 Mar 2007

References

  • Atkinson , K.E. 1996 . The numerical solution of Fredholm integral equations of the second kind , Cambridge University Press .
  • Chen , K. 1996 . On a new preconditioning algorithm for iterative solution of generalized boundary element systems . J. Dalian Univ. Tech , 49 : 1 – 18 . ISSN 1000-8608
  • Chen , K. and Lai , C.H. 1999 . “ Parallel flexible elimination algorithms for solutions of boundary element equations ” . In submitted
  • Dekker , T.J. and Hoffmann , W. 1989 . Rehabilitation of the Gauss-Jordan algorithm . Numer. Math , 54 : 591 – 599 .
  • Dekker , T.J. , Hoffmann , W. and Prota , K. 1994 . Parallel algorithms for solving large linear systems . J. Comput. Appl. Math , 50 : 221 – 232 .
  • Dekker , T.J. , Hoffmann , W. and Prota , K. 1997 . Stability of the Gauss-Huard algorithm with partial pivoting , 58 : 225 – 244 .
  • Evans , D.J. 1998 . “ Parallel implicit schemes for the solution of linear systems ” . In Algorithms for Large Scale Linear Algebraic Systems , Edited by: Althaus , W.G. and Spedicato , E. 37 – 54 . Kluwer Academic Publishers .
  • Evans , D.J. and Barulli , M. 1998 . BSP linear solvers for dense matrices . Para. Comput , 24 : 777 – 795 .
  • Golub , G.H. and Van Loan , C. 1996 . Matrix computation , USA : John Hopkins University Press .
  • Hoffmann , W. 1998 . The Gauss-Huard algorithm and LU factorization . Lin. Alg.App , 275-276 : 275 – 276 . 281-286
  • Hoffmann , W. , Potnia , K. and Pronk , G. 1994 . Solving dense linear systems by Gauss- Huard's method on a distributed memory system . Future Gen. Comp. Sys , 10 : 321 – 325 .
  • Huard , P. 1979 . La methode du simplexe sans inverse explicite . Bull,E. D. F de la Direction des Etudes at des Recherches , 2 ( 2 ) : 79 – 98 .
  • Jawson , M.A. and Symm , G.T. 1977 . Integral equation methods in potential theory and electrostatics , Academic Press .
  • Jumarhon , B. , Arnini , S. and Chen , K. 1998 . On the convergence of the boundary element dual reciprocity method . Eng. Anal. Boun. Elem , 20 : 205 – 211 .
  • Lai , C.H. 1994 . On Purcell's method and the Gauss-Jordan elimination method . Int. J.Math. Educ. Sci. Technol , 25 : 759 – 778 .
  • Lai , C.H. 1997 . On an extension of Purcell's vector method with applications to panel element equations . Compu. Math. Appl , 33 : 101 – 104 .
  • Lai , C.H. and Chen , K. 1998 . Solutions of boundary element equations by a flexible elimination process . Contemp. Math , 218 : 311 – 317 .
  • Melhem , R. 1987 . Parallel Gauss-Jordan elimination for the solution of dense linear systems . Para. Compt , 4 : 339 – 343 .
  • Purcell , E.W. 1953 . The vector method of solving simultaneous linear system . J.Maths. Phys , 32 : 180 – 183 .
  • Stewart , G.W. 1998 . “ Matrix Algorithms ” . In Basic Decompositions , USA : SIAM publications .

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.