On Semismooth Newton’s Methods for Total Variation Minimization

2007 ◽  
Vol 27 (3) ◽  
pp. 265-276 ◽  
Author(s):  
Michael K. Ng ◽  
Liqun Qi ◽  
Yu-fei Yang ◽  
Yu-mei Huang
Keyword(s):  
Total Variation ◽  
Total Variation Minimization ◽  
Newton's Methods

scholarly journals A nonmonotone inexact Newton algorithm for nonlinear systems of equations

1995 ◽  
Vol 36 (4) ◽  
pp. 460-492 ◽  
Author(s):  
Yi Xiao ◽  
Eric King-Wah Chu
Keyword(s):  
Hopf Bifurcation ◽  
Nonlinear Systems ◽  
Numerical Experiments ◽  
Standard Test ◽  
Test Problems ◽  
Systems Of Equations ◽  
Nonlinear Systems Of Equations ◽  
Special Cases ◽  
Nonmonotone Techniques ◽  
Newton's Methods

AbstractIn this paper, an inexact Newton's method for nonlinear systems of equations is proposed. The method applies nonmonotone techniques and Newton's as well as inexact Newton's methods can be viewed as special cases of this new method. The method converges globally and quadratically. Some numerical experiments are reported for both standard test problems and an application in the computation of Hopf bifurcation points.

scholarly journals A New Approach for Solving Dual Fuzzy Nonlinear Equations Using Broyden's and Newton's Methods

2012 ◽  
Vol 2012 ◽  
pp. 1-5 ◽  
Author(s):  
M. Y. Waziri ◽  
Z. A. Majid
Keyword(s):  
Nonlinear Equations ◽  
Newton's Method ◽  
Numerical Results ◽  
Parametric Form ◽  
New Approach ◽  
Broyden’S Method ◽  
Broyden's Method ◽  
Effectiveness And Efficiency ◽  
Initial Iteration ◽  
Newton's Methods

We present a new approach for solving dual fuzzy nonlinear equations. In this approach, we use Newton's method for initial iteration and Broyden's method for the rest of the iterations. The fuzzy coefficients are presented in parametric form. Numerical results on well-known benchmark fuzzy nonlinear equations are reported to authenticate the effectiveness and efficiency of the approach.

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