International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 4, Pages 793-802
doi:10.1155/S0161171284000818
Multiparameter extrapolation and deflation methods for solving equation systems
Department of Economics, Erasmus University, PO Box 1738, DR Rotterdam 3000, The Netherlands
Received 21 May 1984; Revised 9 August 1984
Copyright © 1984 A. J. Hughes Hallett. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Most models in economics and the applied sciences are solved by first order iterative techniques, usually those based on the Gauss-Seidel algorithm. This paper examines the convergence of multiparameter extrapolations (accelerations) of first order iterations, as an improved approximation to the Newton method for solving arbitrary nonlinear equation systems. It generalises my earlier results on single parameter extrapolations. Richardson's generalised method and the deflation method for detecting successive solutions in nonlinear equation systems are also presented as multiparameter extrapolations of first order iterations. New convergence results are obtained for those methods.