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Original Articles

Relaxed parallel two-stage multisplitting methods II: Asynchronous version

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Pages 1277-1287 | Received 28 Nov 2002, Published online: 12 May 2010

References

  • Bai , Z. Z. (1997) . Parallel multisplitting two-stage iterative methods for large sparse systems of weakly nonlinear equations . Numer. Algorithms , 15 : 347 – 372 .
  • Bai , Z. Z. , Wang , D. R. and Evans , D. J. (1995) . Models of asynchronous parallel matrix multisplitting relaxed iterations . Parallel Comput. , 21 : 565 – 582 .
  • Berman A. Plemmons R. J. (1979) Nonnegative Matrices in the Mathematical Science 3rd ed. Academic Press New York
  • Bru , R. , Elsner , L. and Neumann , M. (1988) . Models of parallel chaotic iteration methods . Lin. Alg. Appl. , 103 : 175 – 192 .
  • Bru , R. and Fuster , R. (1990) . Parallel chaotic extrapolated Jacobi method . Appl. Math. Lett. , 3 : 65 – 69 .
  • Bru , R. , Migallon , V. , Penades , J. and Szyld , D. B. (1995) . Parallel synchronous and asynchronous two-stage multisplitting methods . Electron. Trans. Numer. Anal. , 3 : 24 – 38 .
  • Frommer , A. and Mayer , G. (1989) . Convergence of relaxed parallel multisplitting methods . Lin. Alg. Appl. , 119 : 141 – 152 .
  • Frommer , A. and Mayer , G. (1989) . Parallel interval multisplitting . Numer. Math. , 56 : 255 – 267 .
  • Frommer , A. and Szyld , D. B. (1992) . H-splitting and two-stage iterative methods . Numer. Math. , 63 : 345 – 356 .
  • Frommer , A. and Szyld , D. B. (1994) . Asynchronous and two-stage iterative methods . Numer. Math. , 69 : 141 – 153 .
  • Fuster , R. , Migallon , V. and Penades , J. (1996) . Non-stationary parallel multisplitting AOR methods . Electron. Trans. Numer. Anal. , 4 : 1 – 13 .
  • Gu T. X. Liu X. P. (1998) Parallel two-stage multisplitting iterative methods Math. Numerica Sinica 20 2 153 166 (in Chinese)
  • Gu , T. X. , Liu , X. P. and Shen , L. J. (2000) . Relaxed parallel two-stage multisplitting methods . Intern. J. Comput. Math. , 75 : 351 – 367 .
  • Gu T. X. Wang N. Ch. (1996) Parallel multisplitting GAOR methods for solving linear interval equations Mathematica Applicata 9 142 146 in Chinese
  • Gu T. X. Wang N. Ch. (1997) Non-stage multisplitting iterative methods for the parallel solutions of linear systems Chinese J. Engineering Math. 14 4 25 32 (in Chinese)
  • Hadjidimos , A. (1978) . Accelerated overrelaxation method . Math. Comp. , 32 : 149 – 157 .
  • Lanzkron , N. K. , Rose , D. J. and Szyld , D. B. (1991) . Convergence of nested classical iterative methods for linear systems . Numer. Math. , 58 : 685 – 702 .
  • Mas , J. , Migallon , V. , Penades , J. and Szyld , D. B. (1996) . Non-stationary parallel relaxed multisplitting methods . Lin. Alg. Appl. , 241–243 : 733 – 747 .
  • Neumaier , A. (1984) . New techniques for the analysis of linear interval equations . Lin. Alg. Appl. , 58 : 273 – 325 .
  • Neumann , M. and Plemmons , R. J. (1987) . Convergence of parallel multisplitting iterative methods for M-matrices . Lin. Alg. Appl. , 88–89 : 559 – 573 .
  • Nichols , N. K. (1973) . On the convergence of two-stage iterative processes for solving linear equations . SIAM J. Numer. Anal. , 10 : 460 – 469 .
  • O'Leary , P. and White , R. E. (1985) . Multi-splitting of matrices and parallel solutions of linear systems . SIAM J. Alg. Dis. Meth. , 6 : 630 – 640 .
  • Otrga J. M. Rheinboldt W. C. (1989) Iterative Solution of Nonlinear Equations in Several Variables. Prentice-Hall International Inc. New Jersey
  • Szyld , D. B. and Jones , M. T. (1993) . Two-stage and multisplitting methods for the parallel solution of linear systems . SIAM J. Matrix Anal. Appl. , 13 : 671 – 679 .
  • Varga R. S. (1962) Matrix Iterative Analysis Prentice Hall
  • Wang , D. R. (1991) . On the convergence of the parallel multisplitting AOR algorithm . Lin. Alg. Appl. , 154–156 : 473 – 577 .
  • White , R. E. (1989) . Multisplitting with different weighting schemes . SIAM J. Matrix Anal. Appl. , 10 : 481 – 493 .
  • White , R. E. (1990) . Multisplitting of a symmetric positive definite matrix . SIAM J. Matrix Anal. Appl. , 11 : 69 – 82 .
  • Young D. M. (1972) Iterative Solution of Large Linear Systems. Academic Press New York

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