On the Gauss-Newton method for solving equations
نویسندگان
چکیده
منابع مشابه
An 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 کاملNewton - Secant method for solving operator equations ∗
where F is a Fréchet-differentiable operator defined on an open subset D of a Banach space X with values in a Banach space Y . Finding roots of Eq.(1) is a classical problem arising in many areas of applied mathematics and engineering. In this study we are concerned with the problem of approximating a locally unique solution α of Eq.(1). Some of the well known methods for this purpose are the f...
متن کاملOn q-Newton-Kantorovich method for solving systems of equations
Starting from q-Taylor formula for the functions of several variables and mean value theorems in q-calculus which we prove by ourselves, we develop a new methods for solving the systems of equations. We will prove its convergence and we will give an estimation of the error. 2004 Elsevier Inc. All rights reserved.
متن کاملOn a Newton-Like Method for Solving Algebraic Riccati Equations
An exact line search method has been introduced by Benner and Byers [IEEE Trans. Autom. Control, 43 (1998), pp. 101–107] for solving continuous algebraic Riccati equations. The method is a modification of Newton’s method. A convergence theory is established in that paper for the Newton-like method under the strong hypothesis of controllability, while the original Newton’s method needs only the ...
متن کاملOn the iteratively regularized Gauss-Newton method for solving nonlinear ill-posed problems
The iteratively regularized Gauss-Newton method is applied to compute the stable solutions to nonlinear ill-posed problems F (x) = y when the data y is given approximately by yδ with ‖yδ − y‖ ≤ δ. In this method, the iterative sequence {xk} is defined successively by xk+1 = x δ k − (αkI +F (xk)F (xk)) ( F (xk) ∗(F (xk)− y) +αk(xk − x0) ) , where x0 := x0 is an initial guess of the exact solutio...
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: Proyecciones (Antofagasta)
سال: 2012
ISSN: 0716-0917
DOI: 10.4067/s0716-09172012000100002