Convergence behaviour of inexact Newton methods
نویسندگان
چکیده
منابع مشابه
Convergence behaviour of inexact Newton methods
In this paper we investigate local convergence properties of inexact Newton and Newton-like methods for systems of nonlinear equations. Processes with modified relative residual control are considered, and new sufficient conditions for linear convergence in an arbitrary vector norm are provided. For a special case the results are affine invariant.
متن کاملOn Semilocal Convergence of Inexact Newton Methods
Inexact Newton methods are constructed by combining Newton’s method with another iterative method that is used to solve the Newton equations inexactly. In this paper, we establish two semilocal convergence theorems for the inexact Newton methods. When these two theorems are specified to Newton’s method, we obtain a different Newton-Kantorovich theorem about Newton’s method. When the iterative m...
متن کاملOn the Convergence of Inexact Newton Methods
A solid understanding of convergence behaviour is essential to the design and analysis of iterative methods. In this paper we explore the convergence of inexact iterative methods in general, and inexact Newton methods in particular. A direct relationship between the convergence of inexact Newton methods and the forcing terms is presented in both theory and numerical experiments.
متن کاملConvergence analysis of inexact proximal Newton-type methods
We study inexact proximal Newton-type methods to solve convex optimization problems in composite form: minimize x∈Rn f(x) := g(x) + h(x), where g is convex and continuously differentiable and h : R → R is a convex but not necessarily differentiable function whose proximal mapping can be evaluated efficiently. Proximal Newton-type methods require the solution of subproblems to obtain the search ...
متن کاملConvergence of inexact Newton methods for generalized equations
For solving the generalized equation f (x) + F(x) 0, where f is a smooth function and F is a set-valued mapping acting between Banach spaces, we study the inexact Newton method described by ( f (xk)+ D f (xk)(xk+1 − xk)+ F(xk+1)) ∩ Rk(xk, xk+1) = ∅, where D f is the derivative of f and the sequence of mappings Rk represents the inexactness. We show how regularity properties of the mappings f + ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1999
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-99-01135-7