Local convergence of the Gauss-Newton method for injective-overdetermined systems of equations under a majorant condition
نویسنده
چکیده
We present, under a weak majorant condition, a local convergence analysis for the Gauss-Newton method for injective-overdetermined systems of equations in a Hilbert space setting. Our results provide under the same information a larger radius of convergence and tighter error estimates on the distances involved than in earlier studies such us [10, 11, 13, 14, 18]. Special cases and numerical examples are also included in this study.
منابع مشابه
On Local Convergence Analysis of Inexact Newton Method for Singular Systems of Equations under Majorant Condition
We present a local convergence analysis of inexact Newton method for solving singular systems of equations. Under the hypothesis that the derivative of the function associated with the singular systems satisfies a majorant condition, we obtain that the method is well defined and converges. Our analysis provides a clear relationship between the majorant function and the function associated with ...
متن کاملAn Inexact Newton-like conditional gradient method for constrained nonlinear systems
In this paper, we propose an inexact Newton-like conditional gradient method for solving constrained systems of nonlinear equations. The local convergence of the new method as well as results on its rate are established by using a general majorant condition. Two applications of such condition are provided: one is for functions whose the derivative satisfies Hölder-like condition and the other i...
متن کاملLocal convergence analysis of inexact Newton-like methods under majorant condition
We provide a local convergence analysis of inexact Newton–like methods in a Banach space setting under flexible majorant conditions. By introducing center–Lipschitz–type condition, we provide (under the same computational cost) a convergence analysis with the following advantages over earlier work [9]: finer error bounds on the distances involved, and a larger radius of convergence. Special cas...
متن کاملA Gauss - Newton method for convex composite optimization 1
An extension of the Gauss-Newton method for nonlinear equations to convex composite optimization is described and analyzed. Local quadratic convergence is established for the minimization of h o F under two conditions, namely h has a set of weak sharp minima, C, and there is a regular point of the inclusion F(x) E C. This result extends a similar convergence result due to Womersley (this journa...
متن کاملAn Analysis on Local Convergence of Inexact Newton-Gauss Method for Solving Singular Systems of Equations
We study the local convergence properties of inexact Newton-Gauss method for singular systems of equations. Unified estimates of radius of convergence balls for one kind of singular systems of equations with constant rank derivatives are obtained. Application to the Smale point estimate theory is provided and some important known results are extended and/or improved.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Computers & Mathematics with Applications
دوره 66 شماره
صفحات -
تاریخ انتشار 2013