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

Authors:
Nuchun Hu;Weiping Shen;Chong Li
Affiliations:
Department of Mathematics, Zhejiang University, Hangzhou 310027, PR China;Department of Mathematics, Zhejiang University, Hangzhou 310027, PR China;Department of Mathematics, Zhejiang University, Hangzhou 310027, PR China
Venue:
Journal of Computational and Applied Mathematics
Year:
2008

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Abstract

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. Hauszler, A Kantorovich-type convergence analysis for the Gauss-Newton-method, Numer. Math. 48 (1986) 119-125.] and extends the main theorem in [I.K. Argyros, On the Newton-Kantorovich hypothesis for solving equations, J. Comput. Appl. Math. 169 (2004) 315-332]. Furthermore, the radius of convergence ball is also obtained.