On the complexity of extending the convergence region for Traub's method
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Date
2020
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Journal ISSN
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Publisher
Academic Press Inc. apjcs@harcourt.com
Abstract
The convergence region of Traub's method for solving equations is small in general. This fact limits its applicability. We locate a more precise region containing the Traub iterations leading to at least as tight Lipschitz constants as before. Our convergence analysis is finer, and obtained without additional conditions. The new theoretical results are tested on numerical examples that illustrate their superiority over earlier results. © 2019
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Keywords
Newton-Raphson method, Convergence analysis, Convergence region, Lipschitz constant, Newton's methods, Semi-local convergences, Traub's method, Banach spaces
Citation
Journal of Complexity, 2020, 56, , pp. -