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

摘要

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.] 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.