Minimization of functions of several variables by derivative-free methods of the newton type

1974 ◽  
Vol 14 (2) ◽  
pp. 3-16
Author(s):  
H. Schwetlick
Keyword(s):  
Several Variables ◽  
Derivative Free ◽  
Derivative Free Methods ◽  
Minimization Of Functions

An efficient class of fourth-order derivative-free method for multiple-roots

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Sunil Kumar ◽  
Deepak Kumar ◽  
Janak Raj Sharma ◽  
Ioannis K. Argyros
Keyword(s):  
Multiple Root ◽  
Second Step ◽  
Optimal Order ◽  
Multiple Roots ◽  
Nonlinear Functions ◽  
New Methods ◽  
Derivative Free ◽  
Derivative Free Methods ◽  
Derivative Free Method ◽  
Good Number

Abstract Many optimal order multiple root techniques, which use derivatives in the algorithm, have been proposed in literature. Many researchers tried to construct an optimal family of derivative-free methods for multiple roots, but they did not get success in this direction. With this as a motivation factor, here, we present a new optimal class of derivative-free methods for obtaining multiple roots of nonlinear functions. This procedure involves Traub–Steffensen iteration in the first step and Traub–Steffensen-like iteration in the second step. Efficacy is checked on a good number of relevant numerical problems that verifies the efficient convergent nature of the new methods. Moreover, we find that the new derivative-free methods are just as competent as the other existing robust methods that use derivatives.

Production optimization using derivative free methods applied to Brugge field case

2014 ◽  
Vol 114 ◽  
pp. 22-37 ◽  
Author(s):  
Masoud Asadollahi ◽  
Geir Nævdal ◽  
Mohsen Dadashpour ◽  
Jon Kleppe
Keyword(s):  
Production Optimization ◽  
Field Case ◽  
Derivative Free ◽  
Derivative Free Methods

scholarly journals A Family of Derivative-Free Methods with High Order of Convergence and Its Application to Nonsmooth Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Alicia Cordero ◽  
José L. Hueso ◽  
Eulalia Martínez ◽  
Juan R. Torregrosa
Keyword(s):  
Fourth Order ◽  
Order Of Convergence ◽  
Nonsmooth Equations ◽  
Order Convergence ◽  
Linear Combinations ◽  
Numerical Examples ◽  
Derivative Free ◽  
Derivative Free Methods ◽  
Seventh Order ◽  
The Given

A family of derivative-free methods of seventh-order convergence for solving nonlinear equations is suggested. In the proposed methods, several linear combinations of divided differences are used in order to get a good estimation of the derivative of the given function at the different steps of the iteration. The efficiency indices of the members of this family are equal to 1.6266. Also, numerical examples are used to show the performance of the presented methods, on smooth and nonsmooth equations, and to compare with other derivative-free methods, including some optimal fourth-order ones, in the sense of Kung-Traub’s conjecture.

Optimal Derivative-Free Methods for Solving Nonlinear Equations

2011 ◽  
Author(s):  
Alicia Cordero ◽  
José L. Hueso ◽  
Eulalia Martínez ◽  
Juan R. Torregrosa ◽  
Theodore E. Simos ◽  
...  
Keyword(s):  
Nonlinear Equations ◽  
Derivative Free ◽  
Derivative Free Methods

scholarly journals Solving Nonsmooth Equations Using Derivative-Free Methods

2012 ◽  
Vol 3 ◽  
pp. 37-45
Author(s):  
M.S.M. Bahgat ◽  
M.A. Hafiz
Keyword(s):  
Error Analysis ◽  
Nonlinear Equations ◽  
Divided Differences ◽  
Nonsmooth Equations ◽  
Linear Combinations ◽  
Cubic Convergence ◽  
Numerical Examples ◽  
Derivative Free ◽  
Derivative Free Methods ◽  
The Given

In this paper, a family of derivative-free methods of cubic convergence for solving nonlinear equations is suggested. In the proposed methods, several linear combinations of divided differences are used in order to get a good estimation of the derivative of the given function at the different steps of the iteration. The efficiency indices of the members of this family are equal to 1.442. The convergence and error analysis are given. Also, numerical examples are used to show the performance of the presented methods and to compare with other derivative-free methods. And, were applied these methods on smooth and nonsmooth equations.

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