Summary
In this paper we consider an extension to nonlinear algebraic systems of the class of algorithms recently proposed by Abaffy, Broyden and Spedicato for general linear systems. We analyze the convergence properties, showing that under the usual assumptions on the function and some mild assumptions on the free parameters available in the class, the algorithm is locally convergent and has a superlinear rate of convergence (per major iteration, which is computationally comparable to a single Newton's step). Some particular algorithms satisfying the conditions on the free parameters are considered.
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Abaffy, J., Galántai, A. & Spedicato, E. The local convergence of ABS methods for nonlinear algebraic equations. Numer. Math. 51, 429–439 (1987). https://doi.org/10.1007/BF01397545
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DOI: https://doi.org/10.1007/BF01397545