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 Higher-Order Iteration Schemes for Solving Nonlinear Systems of Equations

Mathematics ◽  
2019 ◽  
Vol 7 (10) ◽  
pp. 937 ◽  
Author(s):  
Hessah Faihan Alqahtani ◽  
Ramandeep Behl ◽  
Munish Kansal
Keyword(s):  
Nonlinear Systems ◽  
Convergence Analysis ◽  
Fourth Order ◽  
Numerical Experiments ◽  
Multidimensional Case ◽  
Systems Of Nonlinear Equations ◽  
Systems Of Equations ◽  
Nonlinear Systems Of Equations ◽  
Validity And Reliability ◽  
Mild Conditions

We present a three-step family of iterative methods to solve systems of nonlinear equations. This family is a generalization of the well-known fourth-order King’s family to the multidimensional case. The convergence analysis of the methods is provided under mild conditions. The analytical discussion of the work is upheld by performing numerical experiments on some application oriented problems. Finally, numerical results demonstrate the validity and reliability of the suggested methods.

A NEW DERIVATIVE-FREE CONJUGATE GRADIENT METHOD FOR LARGE-SCALE NONLINEAR SYSTEMS OF EQUATIONS

2017 ◽  
Vol 95 (3) ◽  
pp. 500-511 ◽  
Author(s):  
XIAOWEI FANG ◽  
QIN NI
Keyword(s):  
Nonlinear Systems ◽  
Conjugate Gradient Method ◽  
Conjugate Gradient ◽  
Gradient Method ◽  
Large Scale ◽  
Test Problems ◽  
Systems Of Equations ◽  
Nonlinear Systems Of Equations ◽  
Line Search Method ◽  
Derivative Free

We propose a new derivative-free conjugate gradient method for large-scale nonlinear systems of equations. The method combines the Rivaie–Mustafa–Ismail–Leong conjugate gradient method for unconstrained optimisation problems and a new nonmonotone line-search method. The global convergence of the proposed method is established under some mild assumptions. Numerical results using 104 test problems from the CUTEst test problem library show that the proposed method is promising.

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