Relaxed parallel two-stage multisplitting methods Footnote^∗

^∗Project supported by China State Major Key Project for Basic Researches and Science Foundation of CAEP.

References

• Bai , Z. Z. 1997 . Parallel multisplitting two-stage iterative methods for large sparse systems of weakly nonlinear equations . Numer. Algorithms , 15 : 347 – 372 .
   Web of Science ®Google Scholar
• Bai , Z. Z. , Wang , D. R. and Evans , D. J. 1995 . Models of asynchronous parallel matrix multisplitting relaxed iterations . Parallel Comput. , 21 : 565 – 582 .
   Web of Science ®Google Scholar
• Berman , A. and Plemmons , R. J. 1979 . Nonnegative Matrices in the Mathematical Science , New York : Academic Press .
   Google Scholar
• Bru , R. , Elsner , L. and Neumann , M. 1988 . Models of parallel chaotic iteration methods . Linear Algebra Appl. , 103 : 175 – 192 .
   Web of Science ®Google Scholar
• Bru , R. and Fuster , R. 1990 . Parallel chaotic extrapolated Jacobi method . Appl. Math. Lett. , 3 : 65 – 69 .
   Google Scholar
• 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 .
   Google Scholar
• Frommer , A. and Mayer , G. 1989 . Convergence of relaxed parallel multisplitting methods . Linear Algebra Appl. , 119 : 141 – 152 .
   Web of Science ®Google Scholar
• Frommer , A. and Mayer , G. 1989 . Parallel interval multisplitting . Numer. Math. , 56 : 255 – 267 .
   Web of Science ®Google Scholar
• Frommer , A. and Szyld , D. B. 1992 . H-splitting and two-stage iterative methods . Numer. Math. , 63 : 345 – 356 .
   Web of Science ®Google Scholar
• Frommer , A. and Szyld , D. B. 1994 . Asynchronous and two-stage iterative methods . Numer. Math. , 69 : 141 – 153 .
   Web of Science ®Google Scholar
• Fuster , R. , Migallon , V. and Penades , J. 1996 . Non-stationary parallel multisplitting AOR methods . Electron. Trans. Numer. Anal. , 4 : 1 – 13 .
   Google Scholar
• Gu , T. X. and Liu , X. P. 1998 . Parallel two-stage multisplitting iterative methods . Math. Numerica Sinica , 20 ( 2 ) : 153 – 166 . in Chinese
   Google Scholar
• Gu , T. X. and Wang , N. C. 1995 . Safe Bounds for the solution of nonlinear problems using a relaxed parallel multisplitting methods . Mathematica Applicata , 8 : 351 – 359 .
   Google Scholar
• Gu , T. X. and Wang , N. C. 1996 . Parallel multisplitting GAOR methods for solving linear interval equations . Mathematica Applicata , 9 : 142 – 146 . in Chinese
   Google Scholar
• Gu , T. X. and Wang , N. C. 1997 . Non-stationary two-stage multisplitting iterative methods for the parallel solutions of linear systems . Chinese J. Engineering Math. , 14 ( 4 ) : 25 – 32 . in Chinese
   Google Scholar
• Hadjidimos , A. 1978 . Accelerated Overlaxation method . Math. Comp. , 32 : 149 – 157 .
   Web of Science ®Google Scholar
• 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 .
   Google Scholar
• Mas , J. , Migallon , V. , Penades , J. and Szyld , D. B. 1996 . Nonstationary parallel relaxed multisplitting methods . Linear Algebra Appl. , 24 ( 1-243 ) : 733 – 747 .
   Google Scholar
• Neumaier , A. 1984 . New techniques for the analysis of linear interval equations . Linear Algebra Appl. , 58 : 273 – 325 .
   Web of Science ®Google Scholar
• Neumann , M. and Plemmons , R. J. 1987 . Convergence of parallel multisplitting iterative methods for M-matrices . Linear Algebra Appl. , 8 ( 8-89 ) : 559 – 573 .
   Web of Science ®Google Scholar
• Nichols , N. K. 1973 . On the convergence of two-stage iterative processes for solving linear equations . SIAM J. Numer. Anal. , 10 : 460 – 469 .
   Web of Science ®Google Scholar
• O′ Leary , D. P. and White , R. E. 1985 . Multi-splitting of matrices and parallel solution of linear systems . SIAM J. Alg. Dis. Meth. , 6 : 630 – 640 .
   Google Scholar
• Otega , J. M. and Rheinboldt , W. C. 1989 . Iterative Solution of Nonlinear Equations in Several Variables , New Jersey : Prentice-hall International, Inc. .
   Google Scholar
• 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 .
   Web of Science ®Google Scholar
• Varga , R. S. 1962 . Matrix Iterative Analysis , Prentice Hall .
   Google Scholar
• Wang , D. R. 1991 . On the convergence of the parallel multisplitting AOR algorithm . Linear Algebra Appl. , 154-156 : 473 – 577 .
   Web of Science ®Google Scholar
• White , R. E. 1989 . Multisplitting with different weighting schemes . SIAM J. Matrix Anal. Appl. , 10 : 481 – 493 .
   Web of Science ®Google Scholar
• White , R. E. 1990 . Multisplitting of a symmetric positive definite matrix . SIAM J. Matrix Anal. Appl. , 11 : 69 – 82 .
   Web of Science ®Google Scholar
• Young , D. M. 1972 . Iterative Solutions of Large Linear Systems , New York : Academic Press .
   Google Scholar