NDLI: Weak sufficient convergence conditions and applications for newton methods

Content Provider	Springer Nature Link
Author	Argyros, Ioannis K.
Copyright Year	2004
Abstract	The famous Newton—Kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of Newton method to a solution of an equation in connection with the Lipschitz continuity of the Fréchet-derivative of the operator involved. Using Lipschitz and center-Lipschitz conditions we show that the Newton—Kantorovich hypothesis is weakened. The error bounds obtained under our semilocal convergence result are finer and the information on the location of the solution more precise than the corresponding ones given by the dominating Newton— Kantorovich theorem, and under the same hypotheses/computational cost, since the evaluation of the Lipschitz also requires the evaluation of the center-Lipschitz constant. In the case of local convergence we obtain a larger convergence radius than before. This observation is important in computational mathematics and can be used in connection to projection methods and in the construction of optimum mesh independence refinement strategies.
Starting Page	1
Ending Page	17
Page Count	17
File Format	PDF
ISSN	15985865
Journal	Journal of Applied Mathematics and Computing
Volume Number	16
Issue Number	1-2
e-ISSN	18652085
Language	English
Publisher	Springer-Verlag
Publisher Date	2004-01-01
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Newton-like methods Banach space semilocal/local convergence upper/lower bounds Newton—Kantorovich hypothesis Extrapolation to the limit, deferred corrections Equations with nonlinear operators Newton-type methods Computational Mathematics and Numerical Analysis ApplicationMathematics/Computational Methods of Engineering Theory of Computation Mathematics of Computing
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Computational Mathematics

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