On the generalisation of the basic iterative methods for the solution of linear systems

References

• Avdelas , G. and Hadjidimos , A. 1981 . Optimum accelerated overrelaxation in a special case . Math. Comp , 36 : 183 – 187 .
   Web of Science ®Google Scholar
• Berman , A. and Plemmons , R.J. 1979 . Nonnegative matrices in the Mathematical Sciences , New York : Academic Press .
   Google Scholar
• Hadjidimos , A. 1978 . Accelerated overrelaxation method . Math. Comp , 32 : 149 – 157 .
   Web of Science ®Google Scholar
• Hadjidimos , A. 1980 . Some basic results on M-matrices in connection with the accelerated overrelaxation (AOR) method . Computing , 24 : 259 – 268 .
   Web of Science ®Google Scholar
• Hadjidimos , A. 1981 . “ A new method for the solution of linear systems arising from the discretization of P.D.E.'s ” . In Advances in Computer Methods for Partial Differential Equations , Edited by: Vichnevetsky , R. and Stepleman , R.S. Vol. IV , 74 – 79 . IMACS .
   Google Scholar
• Hadjidimos , A. and Yeyios , A. 1980 . The principle of extrapolation in connection with the accelerated overrelaxation method . Linear Algebra Appl , 30 : 115 – 128 .
   Web of Science ®Google Scholar
• Kahan , W. 1958 . “ Gauss-Seidel methods of solving large systems of linear equations ” . In Ph.D. Thesis , Canada : University of Toronto .
   Google Scholar
• Kulisch , U. 1968 . Über Reguläre Zerlegungen von Matrizen und einige Anwendungen . Numer. Math , 11 : 444 – 449 .
   Google Scholar
• Marek , I. 1970 . Frobenius theory of positive operators: Comparison theorems and applications . SIAM J. Appl. Math , 19 : 607 – 628 .
   Web of Science ®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
• Ortega , J.M. and Plemmons , R.J. 1979 . Extensions of the Ostrowski-Reich theorem for SOR iterations . Linear Algebra Appl , 28 : 177 – 191 .
   Google Scholar
• Plemmons , R.J. 1977 . M-matrix characterizations. I-nonsingular M-matrices . Linear Algebra Appl , 18 : 175 – 188 .
   Web of Science ®Google Scholar
• Sisler , M. 1973 . Über ein Zweiparametriges Iterationsverfahrens . Apl. Mat , 18 : 325 – 332 .
   Google Scholar
• Sisler , M. 1975 . Über die Optimierung eines Zweiparametrigen Iterationsverfahrens . Apl. Mat , 20 : 126 – 142 .
   Google Scholar
• Sisler , M. 1976 . Bemerkungen zur Optimierung eines Zweiparametrigen Iterations-verfahrens . Apl. Mat , 21 : 213 – 220 .
   Google Scholar
• Varga , R.S. 1962 . Matrix iterative analysis , Englewood Cliffs, New Jersey : Prentice-Hall .
   Google Scholar
• Varga , R.S. 1976 . “ M-matrix theory and recent results in numerical linear algebra ” . In Sparse Matrix Computations , Edited by: Bunch , J.R. and Rose , D.J. 375 – 387 . New York : Academic Press .
   Google Scholar
• Varga , R.S. 1976 . On recurring theorems on diagonal dominance . Linear Algebra Appl , 13 : 1 – 9 .
   Web of Science ®Google Scholar
• Young , D.M. 1971 . Iterative Solution of Large Linear Systems , New York : Academic Press .
   Google Scholar