scholarly journals Generalized Newton Method for a Kind of Complementarity Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Shou-qiang Du
Keyword(s):  
Global Convergence ◽  
Newton Method ◽  
Differentiable Function ◽  
Local Convergence ◽  
Complementarity Problem ◽  
Merit Function ◽  
Nonsmooth Equations ◽  
Generalized Newton Method ◽  
Convergence Results ◽  
Generalized Newton

A generalized Newton method for the solution of a kind of complementarity problem is given. The method is based on a nonsmooth equations reformulation of the problem byF-Bfunction and on a generalized Newton method. The merit function used is a differentiable function. The global convergence and superlinear local convergence results are also given under suitable assumptions. Finally, some numerical results and discussions are presented.

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.

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