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Original Articles

Main convergence theorems for the improved sor method with orderings

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Pages 123-147 | Received 27 Mar 1996, Published online: 19 Mar 2007

References

  • Arms , R. J. , Gates , L. D. and Zondek , B. 1956 . A method of block iteration . J. Soc. Indust. Appl. Math. , 4 : 220 – 229 .
  • Bank , R. E. 1977 . Marching algorithms for elliptic boundary value problems. II: The variable coefficient case . SIAM J. Numer. Anal. , 14 : 950 – 970 .
  • Bank , R. E. and Rose , D. J. 1977 . Marching algorithms for elliptic boundary value problems. I: The constant coefficient case . SIAM J. Numer. Anal. , 14 : 792 – 829 .
  • Buoni , J. J. and Varga , R. S. 1979 . “ Theorems of Stein-Rosenberg type ” . In Numerical Mathematics , Edited by: Ansorge , R. , Glashoff , K. and Wener , B. 65 – 75 . Basel : Birkhauser .
  • Ehrlich , L. W. 1981 . An Ad-Hoc SOR method . J. Comput. Phys. , 44 : 31 – 45 .
  • Ehrlich , L. W. 1990 . “ A local relaxation scheme (Ad-Hoc SOR) applied to nine point and block difference equations ” . In Iterative Methods for Large Linear Systems , Edited by: Kincaid , D. and Hayes , L. 81 – 90 . Academic Press .
  • Elman , H. C. and Chernesky , M. P. 1994 . “ Ordering effects on relaxation methods applied to the discrete convection-diffusion ” . In Recent Advances in Iterative Methods Edited by: Golub , G. , Greenbaum , A. and Luskin , M. 45 – 57 .
  • Evans , D. J. and Martins , M. M. 1992 . On the convergence of the extrapolated AOR method . Intern. J. Computer Math. , 43 : 161 – 171 .
  • Fujino , S. and Takeuchi , T. 1994 . ILU factorization well-suited to vector processor by consideration on difference schemes . Transactions of Japan Soc. Indust. Appl. Math. , 4 : 63 – 86 .
  • Friedman B. The iterative solution of elliptic difference equations Report NYO-7698 Institute of Mathematical Science, New York University. 1957
  • Han , H. , Il'in , V. P. , Yuan , W. and Kellogg , R. B. 1992 . Analysis of flow directed iterations . J. Comput. Math. , 10 : 57 – 76 .
  • Heller , J. 1957 . Ordering properties of linear successive iteration schemes applied to multi-diagonal type linear systems . J. Soc. Indust. Appl. Math. , 5 : 238 – 243 .
  • Ishiwata , E. and Muroya , Y. 1995 . “ Improved SOR-like method with orderings for non-symmetric linear equations derived from singular perturbation problems ” . In Numerical Analysis of Ordinary Differential Equations and its Applications , 59 – 73 . Singapore : World Scientific Publishers .
  • Ishiwata E. Muroya Y. Improved SOR method with orderings and direct methods, Tech. Report 95-34 Waseda University. 1995
  • Ishiwata E. Muroya Y. Precise error estimates of the improved SOR method with orderings for tridiagonal matrices Tech. Report, 95-43 Waseda University. 1995
  • Ishiwata E. Muroya Y. The improved SOR method with orderings in n2 cases of one free relaxation parameter for tridiagonal matrices, Tech. Report 95-45 Waseda University. 1995
  • Ishiwata E. Muroya Y. Isogai K. Adaptive improved SOR method with orderings, Tech. Report 96-7 Waseda University. 1996
  • James , K. R. 1973 . Convergence of matrix iterations subject to diagonal dominance . SIAM J. Numer. Anal. , 10 : 478 – 484 .
  • James , K. R. and Riha , A. 1975 . Convergence criteria for successive overrelaxation . SIAM J. Numer. Anal. , 12 : 137 – 143 .
  • Kuo , C. C. J. , Levy , B. C. and Musicus , B. R. 1987 . A local relaxation method for solving elliptic PDEs on mesh-connected arrays . SIAM J. Sci. Stat. Comput. , 8 : 550 – 573 .
  • Lynch , R. E. , Rice , J. R. and Thomas , D. H. 1964 . Direct solution of partial difference equations by tensor product methods . Numer. Math. , 6 : 185 – 199 .
  • Lynch , R. E. , Rice , J. R. and Thomas , D. H. 1964 . Tensor product analysis of partial difference equations . Bull. Amer. Math. Soc. , 70 : 378 – 384 .
  • Varga , R. S. 1962 . Matrix iterative analysis , Englewood Cliffs, New Jersey : Prentice-Hall Inc. .
  • Young , D. M. 1971 . Iterative solution of large linear systems , New York : Academic Press .

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