On exact convergence of the accelerated overrelaxation method when applied to consistently ordered systems

References

• Hadjidimos , A. 1978 . Accelerated overrelaxation method . Math. Comp. , 32 : 149 – 157 .
   Web of Science ®Google Scholar
• Sisler , M. 1973 . Uber ein Zweiparametriges Iterationsverfahren . Apl. Math. , 18 : 325 – 332 .
   Google Scholar
• Niethammer , W. 1979 . On different splittings and the associated iteration methods . SIAM J. Numer. Anal. , 16 : 186 – 200 .
   Web of Science ®Google Scholar
• Yeyios A. On the accelerated overrelaxation (AOR) method for solving large linear systems University of Ioanina Greece 1979 Ph. D. Dissertation
   Google Scholar
• Hadjidimos , A. and Yeyios , A. 1980 . The principle of extrapolation in connection with the accelerated overrelaxation method . Lin. Alg. Appl. , 30 : 115 – 128 .
   Web of Science ®Google Scholar
• Hadjidimos , A. and Yeyios , A. 1982 . On some extensions of the accelerated overrelaxation (AOR) theory . Intern. J. Math. Math. Sc. , 5 : 49 – 60 .
   Google Scholar
• Martins , M. M. 1980 . On an accelerated overrelaxation iterative method for linear systems with strictly diagonally dominant matrix . Math. Comp. , 35 : 1269 – 1273 .
   Web of Science ®Google Scholar
• Martins , M. M. 1981 . Note on irreducible diagonally dominant matrices and the convergence of the AOR iterative method . Math. Comp. , 37 : 101 – 103 .
   Web of Science ®Google Scholar
• Martins , M. M. 1982 . Generalized diagonal dominance in connection with the accelerated overrelaxation (AOR) method . BIT , 22 : 73 – 78 .
   Web of Science ®Google Scholar
• Yamada , S. , Ikeuchi , M. , Sawami , H. and Niki , H. 1981 . Convergence rate of accelerated overrelaxation method . Proc. 23rd Nat. Meet. Info. Soc. Japan . 1981 , Tokyo, Japan.
   Google Scholar
• Avdelas , G. and Hadjidimos , A. 1981 . Optimum accelerated overrelaxation method in a special case . Math. Comp. , 36 : 183 – 187 .
   Web of Science ®Google Scholar
• Missirlis , N. and Evans , D. J. 1981 . On the convergence of some generalized preconditioned iterative methods . SIAM J. Numer. Anal. , 18 : 591 – 596 .
   Web of Science ®Google Scholar
• Missirlis , N. and Evans , D. J. 1982 . On the dynamic acceleration of the preconditioned simultaneous displacement (PSD) method . Int. J. Comp. Math. , 10 : 153 – 176 .
   Google Scholar
• Gaitanos , N. , Hadjidimos , A. and Yeyios , A. 1983 . Optimum accelerated overrelaxation (AOR) method for systems with positive definite coefficient matrix . SIAM J. Numer. Anal. , 20 : 774 – 783 .
   Web of Science ®Google Scholar
• Papatheodorou , T. S. 1983 . Block AOR iteration for nonsymmetric matrices . Math. Comp. , 41 : 511 – 525 .
   Web of Science ®Google Scholar
• Missirlis , N. M. 1984 . Convergence theory of extrapolated iterative methods for a certain class of nonsymmetric linear systems . Num. Math. , 45 : 447 – 458 .
   Google Scholar
• Albrecht , P. and Klein , M. P. 1984 . Extrapolated iterative methods for linear systems . SIAM J. Numer. Anal. , 21 : 192 – 201 .
   Web of Science ®Google Scholar
• Hadjidimos , A. , Psimarni , A. and Yeyios , A. 1986 . On the convergence of some generalized iterative methods . Lin. Alg. Appl. , 75 : 117 – 132 .
   Web of Science ®Google Scholar
• Hadjidimos , A. , Papatheodorou , T. S. and Saridakis , Y. G. in press . Optimal block iterative schemes for certain large, sparse and nonsymmetric systems . Lin. Alg. Appl. ,
   Google Scholar
• Papadopoulou , E. P. , Papatheodorou , T. S. and Saridakis , Y. G. in press . Block AOR iterative schemes for large-scale least-squares problems . SIAM J. Num. Anal. ,
   Google Scholar
• Saridakis , Y. G. and Papatheodorou , T. S. in press . Optimal block accelerated overrelaxation method for a large class of 2-cyclic matrices . Intern. J. Comp. Math. ,
   Google Scholar
• Saridakis Y. G. Parallelism, applicability and optimality of modern iterative methods Clarkson University 1985 Ph. D. Dissertation
   Google Scholar
• Saridakis , Y. G. 1986 . Generalized consistent orderings and the accelerated overrelaxation method . BIT , 26 : 369 – 376 .
   Web of Science ®Google Scholar
• Saridakis , Y. G. in press . An algorithmic approach for the analysis of extrapolated iterative schemes applied to least-squares problems . J. Comp. Appl. Math. ,
   Google Scholar
• Young D. M. Iterative methods for solving partial difference equations of elliptic type Harvard University 1950 Ph. D. Dissertation
   Google Scholar
• Young , D. M. 1954 . Iterative methods for solving partial difference equations of elliptic type . Trans. Amer. Math. Soc. , 76 : 92 – 111 .
   Web of Science ®Google Scholar
• Verner , J. H. and Bernal , M. J. M. 1968 . On generalizations of the theory of consistent orderings for successive overrelaxation methods . Num. Math. , 12 : 215 – 222 .
   Google Scholar
• Varga , R. S. 1959 . p-Cyclic matrices: A generalization of the Young-Frankel successive overrelaxation scheme . Pac. J. Math. , 9 : 617 – 628 .
   Google Scholar
• Kjellberg , G. 1961 . On the successive over-relaxation method for cyclic operators . Num. Math. , 3 : 87 – 91 .
   Google Scholar
• Broyden , C. G. 1964 . Some generalizations of the theory of successive over-relaxation . Num. Math. , 6 : 269 – 284 .
   Google Scholar
• Young , D. M. 1971 . Iterative Solution of Large Linear Systems , New York : Academic Press .
   Google Scholar
• Varga , R. S. 1962 . Matrix Iterative Analysis , Englewood Cliffs, New Jersey : Prentice-Hall .
   Google Scholar
• Saridakis , Y. G. and Varga , R. S. “ Regions of exact convergence of the USSOR method applied on generalized consistently ordered matrices ” . to appear
   Google Scholar
• Neumaier , A. and Varga , R. S. 1984 . Exact convergence and divergence domains for the SSOR method applied to H-matrices . Lin. Alg. Appl. , 58 : 261 – 272 .
   Web of Science ®Google Scholar