On the solution of systems of equations by the epsilon algorithm of Wynn
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 Math. Comp. 26 (1972), 427436 Request permission
Abstract:
The $\epsilon$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 ${{\text {x}}_{i + 1}} = F({{\text {x}}_i})$ of an analytic function $F:{{\text {R}}^n} \supset D \to {{\text {R}}^n}$ provides a quadratically convergent iterative method; furthermore, no differentiation of $F$ is needed. Some examples illustrate the numerical performance of this method and show that convergence can be obtained even when $F$ is not contractive near the fixed point. A modification of the method is discussed and illustrated.References

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Additional Information
 © Copyright 1972 American Mathematical Society
 Journal: Math. Comp. 26 (1972), 427436
 MSC: Primary 65B99
 DOI: https://doi.org/10.1090/S0025571819720314226X
 MathSciNet review: 0314226