The convergence of accelerated overrelaxation iterations
Author:
A. J. HughesHallett
Journal:
Math. Comp. 47 (1986), 219223
MSC:
Primary 65F10
Corrigendum:
Math. Comp. 51 (1988), 387.
Corrigendum:
Math. Comp. 51 (1988), 387388.
MathSciNet review:
842131
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Abstract 
References 
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Abstract: Accelerated Overrelaxation Iterations extrapolate the standard Successive Overrelaxation Iterations. This paper provides conditions for the convergence of the Accelerated Overrelaxation process; and a conditionally optimal version is derived for solving an arbitrary real linear equation system.
 [1]
P. G. Fisher, S. Holly & A. J. Hughes Hallett, Efficient Solution Techniques for Dynamic Rational Expectations Models, Paper presented to the Econometric Society World Congress, Cambridge, Mass.; and Macroeconomic Modelling Bureau Discussion Paper No. 4, University of Warwick, England.
 [2]
Apostolos
Hadjidimos, Accelerated overrelaxation
method, Math. Comp. 32
(1978), no. 141, 149–157. MR 0483340
(58 #3353), http://dx.doi.org/10.1090/S00255718197804833406
 [3]
A.
Hadjidimos, The optimal solution of the extrapolation problem of a
first order scheme, Internat. J. Comput. Math. 13
(1983), no. 2, 153–168. MR 701765
(84g:65044), http://dx.doi.org/10.1080/00207168308803360
 [4]
A. J. Hughes Hallett, Some Extensions and Comparisons in the Theory of GaussSeidel Iterative Techniques for Solving Large Equation Systems (E. G. Charatsis, ed.), Proceedings of the Econometric Society European Meeting, 1979, NorthHolland, Amsterdam, 1981.
 [5]
A.
J. Hughes Hallett, Alternative techniques for solving systems of
nonlinear equations, J. Comput. Appl. Math. 8 (1982),
no. 1, 35–48. MR 653374
(83d:65163), http://dx.doi.org/10.1016/0771050X(82)900055
 [6]
A.
J. HughesHallett, Simple and optimal extrapolations for first
order iterations, Internat. J. Comput. Math. 15
(1984), no. 34, 309–318. MR 754273
(85k:65028), http://dx.doi.org/10.1080/00207168408803417
 [7]
A.
J. HughesHallett, Techniques which accelerate the convergence of
first order iterations automatically, Linear Algebra Appl.
68 (1985), 115–130. MR 794818
(86h:65042), http://dx.doi.org/10.1016/00243795(85)902101
 [8]
Eugene
Isaacson and Herbert
Bishop Keller, Analysis of numerical methods, John Wiley &
Sons, Inc., New YorkLondonSydney, 1966. MR 0201039
(34 #924)
 [9]
David
M. Young, Iterative solution of large linear systems, Academic
Press, New YorkLondon, 1971. MR 0305568
(46 #4698)
 [1]
 P. G. Fisher, S. Holly & A. J. Hughes Hallett, Efficient Solution Techniques for Dynamic Rational Expectations Models, Paper presented to the Econometric Society World Congress, Cambridge, Mass.; and Macroeconomic Modelling Bureau Discussion Paper No. 4, University of Warwick, England.
 [2]
 A. Hadjidimos, "Accelerated overrelaxation method," Math. Comp., v. 32, 1978, pp. 149157. MR 0483340 (58:3353)
 [3]
 A. Hadjidimos, "The optimal solution of the extrapolation problem of a first order scheme," Internat. J. Comput. Math., v. 15, 1983, pp. 153168. MR 701765 (84g:65044)
 [4]
 A. J. Hughes Hallett, Some Extensions and Comparisons in the Theory of GaussSeidel Iterative Techniques for Solving Large Equation Systems (E. G. Charatsis, ed.), Proceedings of the Econometric Society European Meeting, 1979, NorthHolland, Amsterdam, 1981.
 [5]
 A. J. Hughes Hallett, "Alternative techniques for solving systems of nonlinear equations," J. Comput. Appl. Math., v. 8, 1982, pp. 3548. MR 653374 (83d:65163)
 [6]
 A. J. Hughes Hallett, "Simple and optimal extrapolations for first order iterations," Internat. J. Comput. Math., v. 15, 1984, pp. 309318. MR 754273 (85k:65028)
 [7]
 A. J. Hughes Hallett, "Techniques which accelerate the convergence of first order iterations automatically," Linear Algebra Appl., v. 68, 1984, pp. 115130. MR 794818 (86h:65042)
 [8]
 E. Isaacson & H. B. Keller, Analysis of Numerical Methods, Wiley, New York, 1966. MR 0201039 (34:924)
 [9]
 D. M. Young, Iterative Solution of Large Linear Systems, Academic Press, New York, 1971. MR 0305568 (46:4698)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198608421319
PII:
S 00255718(1986)08421319
Article copyright:
© Copyright 1986
American Mathematical Society
