Abstract
The convergence domain for both the local and semilocal case of Newton’s method for Banach space valued operators is small in general. There is a plethora of articles that have extended the convergence criterion due to Kantorovich under variations of the convergence conditions. In this article, we use a different approach than before to increase the convergence domain, and without necessarily using conditions on the inverse of the Fréchet-derivative of the operator involved. Favorable to us applications are given to test the convergence criteria.
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Argyros, I.K., Magreñán, Á.A., Yáñez, D.F. et al. A new technique for studying the convergence of Newton’s solver with real life applications. J Math Chem 58, 816–830 (2020). https://doi.org/10.1007/s10910-020-01119-0
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DOI: https://doi.org/10.1007/s10910-020-01119-0