The convergence of accelerated overrelaxation iterations

Author:
A. J. Hughes-Hallett

Journal:
Math. Comp. **47** (1986), 219-223

MSC:
Primary 65F10

DOI:
https://doi.org/10.1090/S0025-5718-1986-0842131-9

Corrigendum:
Math. Comp. **51** (1988), 387.

Corrigendum:
Math. Comp. **51** (1988), 387-388.

MathSciNet review:
842131

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Abstract | References | Similar Articles | Additional Information

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]**A. Hadjidimos, "Accelerated overrelaxation method,"*Math. Comp.*, v. 32, 1978, pp. 149-157. 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. 153-168. MR**701765 (84g:65044)****[4]**A. J. Hughes Hallett,*Some Extensions and Comparisons in the Theory of Gauss-Seidel Iterative Techniques for Solving Large Equation Systems*(E. G. Charatsis, ed.), Proceedings of the Econometric Society European Meeting, 1979, North-Holland, Amsterdam, 1981.**[5]**A. J. Hughes Hallett, "Alternative techniques for solving systems of nonlinear equations,"*J. Comput. Appl. Math.*, v. 8, 1982, pp. 35-48. 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. 309-318. 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. 115-130. 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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DOI:
https://doi.org/10.1090/S0025-5718-1986-0842131-9

Article copyright:
© Copyright 1986
American Mathematical Society