Nondiscrete induction and an inversion-free modification of Newton's method
Florian-Alexandru Potra, Vlastimil Pták (1983)
Časopis pro pěstování matematiky
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Florian-Alexandru Potra, Vlastimil Pták (1983)
Časopis pro pěstování matematiky
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Ioannis K. Argyros, Saïd Hilout (2013)
Czechoslovak Mathematical Journal
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We extend the applicability of Newton's method for approximating a solution of a nonlinear operator equation in a Banach space setting using nondiscrete mathematical induction concept introduced by Potra and Pták. We obtain new sufficient convergence conditions for Newton's method using Lipschitz and center-Lipschitz conditions instead of only the Lipschitz condition used in F. A. Potra, V. Pták, Sharp error bounds for Newton's process, Numer. Math., 34 (1980), 63–72, and F. A. Potra,...
Florian-Alexandru Potra (1981)
Aplikace matematiky
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Erich Bohl, Johannes Schropp (1993)
Applications of Mathematics
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We prove a convergence result for a time discrete process of the form under weak conditions on the function . This result is a slight generalization of the convergence result given in [5].Furthermore, we discuss applications to minimizing problems, boundary value problems and systems of nonlinear equations.
Ioannis K. Argyros, Santhosh George (2015)
Applicationes Mathematicae
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We present a local convergence analysis of inexact Newton-like methods for solving nonlinear equations. Using more precise majorant conditions than in earlier studies, we provide: a larger radius of convergence; tighter error estimates on the distances involved; and a clearer relationship between the majorant function and the associated least squares problem. Moreover, these advantages are obtained under the same computational cost.
Argyros, I.K., Hilout, S. (2009)
Surveys in Mathematics and its Applications
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