scholarly journals On generalized Newton method for solving operator inclusions

Filomat ◽  
2012 ◽  
Vol 26 (5) ◽  
pp. 1055-1063 ◽  
Author(s):  
D.R. Sahu ◽  
Kumar Singh
Keyword(s):  
Newton Method ◽  
Existence And Uniqueness ◽  
Maximal Monotone ◽  
Generalized Newton Method ◽  
Existence And Uniqueness Theorem ◽  
Open Convex ◽  
Math Programming ◽  
Generalized Operator ◽  
Generalized Newton ◽  
Open Convex Subset

In this paper, we study the existence and uniqueness theorem for solving the generalized operator equation of the form F(x) + G(x) + T(x) ? 0, where F is a Fr?chet differentiable operator, G is a maximal monotone operator and T is a Lipschitzian operator defined on an open convex subset of a Hilbert space. Our results are improvements upon corresponding results of Uko [Generalized equations and the generalized Newton method, Math. Programming 73 (1996) 251-268].

scholarly journals A Newton-type method and its application

2006 ◽  
Vol 2006 ◽  
pp. 1-9 ◽  
Author(s):  
V. Antony Vijesh ◽  
P. V. Subrahmanyam
Keyword(s):  
Existence And Uniqueness ◽  
Functional Integral ◽  
Existence And Uniqueness Theorem ◽  
Open Convex ◽  
Type Method ◽  
Nonlinear Functional ◽  
Recent Theorem ◽  
Urysohn Operator ◽  
Functional Integral Equations ◽  
Open Convex Subset

We prove an existence and uniqueness theorem for solving the operator equationF(x)+G(x)=0, whereFis a continuous and Gâteaux differentiable operator and the operatorGsatisfies Lipschitz condition on an open convex subset of a Banach space. As corollaries, a recent theorem of Argyros (2003) and the classical convergence theorem for modified Newton iterates are deduced. We further obtain an existence theorem for a class of nonlinear functional integral equations involving the Urysohn operator.

scholarly journals A Generalized Inexact Newton Method for Inverse Eigenvalue Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Weiping Shen
Keyword(s):  
Newton Method ◽  
Quadratic Convergence ◽  
Eigenvalue Problems ◽  
Generalized Newton Method ◽  
Inexact Newton Method ◽  
Numerical Tests ◽  
Inverse Eigenvalue Problems ◽  
Inverse Eigenvalue ◽  
Generalized Newton ◽  
Special Case

We propose a generalized inexact Newton method for solving the inverse eigenvalue problems, which includes the generalized Newton method as a special case. Under the nonsingularity assumption of the Jacobian matrices at the solutionc*, a convergence analysis covering both the distinct and multiple eigenvalue cases is provided and the quadratic convergence property is proved. Moreover, numerical tests are given in the last section and comparisons with the generalized Newton method are made.

scholarly journals A Two-Step Newton-Type Method for Solving System of Absolute Value Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Lei Shi ◽  
Javed Iqbal ◽  
Muhammad Arif ◽  
Alamgir Khan
Keyword(s):  
Newton Method ◽  
New Method ◽  
Generalized Newton Method ◽  
Absolute Value Equations ◽  
Step Method ◽  
Type Method ◽  
Numerical Examples ◽  
Absolute Value ◽  
Generalized Newton

In this paper, we suggest a Newton-type method for solving the system of absolute value equations. This new method is a two-step method with the generalized Newton method as predictor. Convergence of the proposed method is proved under some suitable conditions. At the end, we take several numerical examples to show that the new method is very effective.

Parameter Estimation for Excavator Arm Using Generalized Newton Method

2004 ◽  
Vol 20 (4) ◽  
pp. 762-767 ◽  
Author(s):  
Y.H. Zweiri ◽  
L.D. Seneviratne ◽  
K. Althoefer
Keyword(s):  
Parameter Estimation ◽  
Newton Method ◽  
Generalized Newton Method ◽  
Generalized Newton

Remarks on the generalized Newton method

1993 ◽  
Vol 59 (1-3) ◽  
pp. 405-412 ◽  
Author(s):  
Livinus Ugochukwu Uko
Keyword(s):  
Newton Method ◽  
Generalized Newton Method ◽  
Generalized Newton
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