Convergence criterion of Newton’s method for singular systems with constant rank derivatives
نویسندگان
چکیده
Article history: Received 14 August 2007 Available online 10 April 2008 Submitted by T.D. Benavides
منابع مشابه
Convergence behavior of Gauss-Newton's method and extensions of the Smale point estimate theory
The notions of Lipschitz conditions with L average are introduced to the study of convergence analysis of Gauss-Newton’s method for singular systems of equations. Unified convergence criteria ensuring the convergence of Gauss-Newton’s method for one kind of singular systems of equations with constant rank derivatives are established and unified estimates of radii of convergence balls are also o...
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The convergence properties of Newton’s method for systems of equations with constant rank derivatives are studied under the hypothesis that the derivatives satisfy some weak Lipschitz conditions. The unified convergence results, which include Kantorovich type theorems and Smale’s point estimate theorems as special cases, are obtained. Mathematics subject classification: 49M15, 65F20, 65H10.
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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. Häußler, A Kantorovich-type convergence analysis for the Gauss–Newton-method, Numer. Math. 48 (1986) 119–125...
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تاریخ انتشار 2008