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Original Articles

A vectorizable variant of pgcr methods for unsymmetric linear systemsFootnote

Pages 291-300 | Received 13 May 1991, Published online: 19 Mar 2007

References

  • Evans , D. J. 1985 . Group explicit iterative methods for solving large linear system . Intern. J. Computer Math. , 17 : 87 – 108 .
  • Evans D. J. New parallel algorithms for partial differential equation Int. Conf. ;Parallel. Computing" 83
  • van der Vorst , Henk A. 1982 . A vectorizable variant of some ICCG methods . SIAM J. Sci. Stat. Comput. , 3 ( 3 ) : 350 – 356 .
  • van der Vorst , Henk A. 1986 . The performance of FORTRAN implementations for preconditioned conjugate gradients on vector computers . Parallel Computing , 3 ( 3 ) : 49 – 58 .
  • Johnson , Olin G. 1983 . Charles A. Micchelli and George Paul, Polynomial preconditions for conjugate gradient calculations . SIAM J. Numer. Anal. , 20 ( 2 ) : 363 – 376 .
  • Radicati di Vrozolo , G. and Robert , Y. 1989 . Parallel conjugate gradient-like algorithms for solving sparse nonsymmetric linear systems on a vector multiprocessor . Parallel Computing , 11 ( 2 ) : 223 – 239 .
  • Brugnano , L. and Marrone , M. 1990 . Vectorization of some block preconditioned conjugate gradient methods . Parallel Computing , 14 ( 2 ) : 191 – 198 .
  • Chronopoulos , A. T. 1989 . On the efficient implementation of preconditioned s-step conjugate gradient methods on multiprocessors with memory hierarchy . Parallel Computing , 11 ( 2 ) : 37 – 53 .
  • Eijkhout , V. and Vassilevski , P. 1989 . Positive definiteness aspects of vectorizable preconditions . Parallel Computing , 10 ( 2 ) : 93 – 100 .
  • Wong , Yau Shu . 1988 . Preconditioned gradient type methods applied to nonsymmetric linear systems . Intern. J. Computer Math. , 23 ( 2 ) : 141 – 165 .
  • Eisenstat , Stanley C. , Elman , Howard C. and Schultz , Marth H. 1983 . Variational iterative methods for nonsymmetric systems of linear equations . SIAM J. Numer. Anal. , 20 ( 2 ) : 345 – 357 .
  • Jia-gan , Hu . 1984 . The estimates of ‖M −1 N‖∞ and the optimally scaled matrix . J. Comput. Math. , 2 ( 2 ) : 122 – 129 .
  • Jia-gan , Hu . 95-104 . Seven-diagonal and nine-diagonal SIP Algorithms . J. Comput. Math. , 5 ( 2 )
  • Missirlis , N. M. 1983 . Convergence of a parallel Jacobi-type method . Intern. J. Computer Math. , 14 ( 2 ) : 371 – 384 .
  • Young , D. M. 1971 . Iterative Solution of Large Linear System , New York : Academic Press .
  • Varga , R. S. 1962 . Matrix Iterative Analysis , Prentice-Hall .
  • James M. Ortega Parallel and Vector Solution of Linear Systems University of Virginia 1986 report
  • Xing-ping , Liu . 1989 . Accelerated SIP algorithms and convergence . Chinese J. Num. Math. & Appl. , 11 ( 1 ) : 70 – 81 .
  • Rodrigue , G. and Wolitezr , D. 1981 . Incomplete block cyclic reduction, 2nd IMACS . International Symposium on parallel computation . 1981 , Newark, Delaware.
  • Xing-ping , Liu . Parallel iterative algorithms for elliptic difference equation . J. Numer. Method & Comput. Appl. , to appear)

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