Abstract
In this study, we use a convex acceleration of Newton's method (or super-Halley method) to approximate solutions of nonlinear equations. We provide sufficient convergence conditions for this method in three space settings: real line, complex plane, and Banach space. Several applications of our results are also provided.
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Ezquerro, J.A., Hernández, M.A. On a Convex Acceleration of Newton's Method. Journal of Optimization Theory and Applications 100, 311–326 (1999). https://doi.org/10.1023/A:1021730118905
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DOI: https://doi.org/10.1023/A:1021730118905