Convergence of Newton's Method for Systems of Equations with Constant Rank Derivatives

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Abstract

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.

Keywords:

Newton's method Overdetermined system Lipschitz condition with $L$ average Convergence Rank.
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Convergence of Newton’s Method for Systems of Equations with Constant Rank Derivatives. (2021). Journal of Computational Mathematics, 25(6), 705-718. https://www.global-sci.com/index.php/JCM/article/view/11860