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Kantorovich's type theorems for systems of equations with constant rank derivatives

✍ Scribed by Nuchun Hu; Weiping Shen; Chong Li

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
197 KB
Volume
219
Category
Article
ISSN
0377-0427

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✦ Synopsis

The famous Newton-Kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of Newton's method to a solution of an equation. Here we present a "Kantorovich type" convergence analysis for the Gauss-Newton's method which improves the result in [W.M. HÀußler, A Kantorovich-type convergence analysis for the Gauss-Newton-method, Numer. Math. 48 (

πŸ“œ SIMILAR VOLUMES

Newton's Method for Analytic Systems of
Newton's Method for Analytic Systems of Equations with Constant Rank Derivatives
✍ Jean-Pierre Dedieu; Myong-Hi Kim πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 154 KB

In this paper we study the convergence properties of Newton's sequence for analytic systems of equations with constant rank derivatives. Our main result is an alpha-theorem which ensures the convergence of Newton's sequence to a leastsquare solution of this system.