On the solution of systems of equations by the epsilon algorithm of Wynn

Author:
E. Gekeler

Journal:
Math. Comp. **26** (1972), 427-436

MSC:
Primary 65B99

DOI:
https://doi.org/10.1090/S0025-5718-1972-0314226-X

MathSciNet review:
0314226

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Abstract | References | Similar Articles | Additional Information

Abstract: The -algorithm has been proposed by Wynn on a number of occasions as a convergence acceleration device for vector sequences; however, little is known concerning its effect upon systems of equations. In this paper, we prove that the algorithm applied to the Picard sequence of an analytic function provides a quadratically convergent iterative method; furthermore, no differentiation of is needed. Some examples illustrate the numerical performance of this method and show that convergence can be obtained even when is not contractive near the fixed point. A modification of the method is discussed and illustrated.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1972-0314226-X

Keywords:
-algorithm,
acceleration of the convergence of sequences,
quadratic convergent iterative method without differentiation,
solution of equations

Article copyright:
© Copyright 1972
American Mathematical Society