On a new class of splitting type iterative methods

2003 ◽  
Author(s):  
R Ciegis
Keyword(s):  
Iterative Methods ◽  
New Class ◽  
Splitting Type

scholarly journals A Family of Fourteenth-Order Convergent Iterative Methods for Solving Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Fiza Zafar ◽  
Gulshan Bibi
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Nonlinear Equations ◽  
Order Of Convergence ◽  
Efficiency Index ◽  
Numerical Examples ◽  
New Class ◽  
First Derivative ◽  
New Methods ◽  
Specific Step

We present a family of fourteenth-order convergent iterative methods for solving nonlinear equations involving a specific step which when combined with any two-step iterative method raises the convergence order by n+10, if n is the order of convergence of the two-step iterative method. This new class include four evaluations of function and one evaluation of the first derivative per iteration. Therefore, the efficiency index of this family is 141/5 =1.695218203. Several numerical examples are given to show that the new methods of this family are comparable with the existing methods.

scholarly journals Trifunction Bihemivariational Inequalities

2021 ◽  
pp. 287-313
Author(s):  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor
Keyword(s):  
Convergence Analysis ◽  
Iterative Methods ◽  
Hemivariational Inequalities ◽  
Auxiliary Principle ◽  
Auxiliary Principle Technique ◽  
New Class ◽  
Mild Conditions ◽  
Special Cases

In this paper, we consider a new class of hemivariational inequalities, which is called the trifunction bihemivariational inequality. We suggest and analyze some iterative methods for solving the trifunction bihemivariational inequality using the auxiliary principle technique. The convergence analysis of these iterative methods is also considered under some mild conditions. Several special cases are also considered. Results proved in this paper can be viewed as a refinement and improvement of the known results.

scholarly journals A new class of parallel alternating-type iterative methods

1996 ◽  
Vol 74 (1-2) ◽  
pp. 331-344 ◽  
Author(s):  
David M. Young ◽  
David R. Kincaid
Keyword(s):  
Iterative Methods ◽  
New Class

scholarly journals Iterative Schemes for a Class of Mixed Trifunction Variational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
Eisa Al-Said
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Iterative Methods ◽  
Auxiliary Principle ◽  
Auxiliary Principle Technique ◽  
Iterative Schemes ◽  
New Class ◽  
Special Cases

We use the auxiliary principle technique to suggest and analyze some iterative methods for solving a new class of variational inequalities, which is called the mixed trifunction variational inequality. The mixed trifunction variational inequality includes the trifunction variational inequalities and the classical variational inequalities as special cases. Convergence of these iterative methods is proved under very mild and suitable assumptions. Several special cases are also considered. Results proved in this paper continue to hold for these known and new classes of variational inequalities and its variant forms.

scholarly journals Some Aspects of Extended General Variational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Muhammad Aslam Noor
Keyword(s):  
Sensitivity Analysis ◽  
Variational Inequalities ◽  
Iterative Methods ◽  
Optimization Problems ◽  
Future Research ◽  
Auxiliary Principle Technique ◽  
New Class ◽  
General Variational Inequality ◽  
General Variational Inequalities ◽  
Novel Applications

Noor (“Extended general variational inequalities,” 2009, “Auxiliary principle technique for extended general variational inequalities,” 2008, “Sensitivity analysis of extended general variational inequalities,” 2009, “Projection iterative methods for extended general variational inequalities,” 2010) introduced and studied a new class of variational inequalities, which is called the extended general variational inequality involving three different operators. This class of variational inequalities includes several classes of variational inequalities and optimization problems. The main motivation of this paper is to review some aspects of these variational inequalities including the iterative methods and sensitivity analysis. We expect that this paper may stimulate future research in this field along with novel applications.

scholarly journals Some Class of Third- and Fourth-Order Iterative Methods for Solving Nonlinear Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
J. P. Jaiswal
Keyword(s):  
Iterative Methods ◽  
Nonlinear Equations ◽  
Fourth Order ◽  
Basins Of Attraction ◽  
Order Method ◽  
Third Order ◽  
Numerical Examples ◽  
Multivariate Extension ◽  
New Class ◽  
Fourth Order Method

The object of the present work is to give the new class of third- and fourth-order iterative methods for solving nonlinear equations. Our proposed third-order method includes methods of Weerakoon and Fernando (2000), Homeier (2005), and Chun and Kim (2010) as particular cases. The multivariate extension of some of these methods has been also deliberated. Finally, some numerical examples are given to illustrate the performances of our proposed methods by comparing them with some well existing third- and fourth-order methods. The efficiency of our proposed fourth-order method over some fourth-order methods is also confirmed by basins of attraction.

scholarly journals Some Iterative Methods for Solving Nonconvex Bifunction Equilibrium Variational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Muhammad Aslam Noor ◽  
Khalida Inayat Noor ◽  
Saira Zainab
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Iterative Methods ◽  
Equilibrium Problems ◽  
Implicit Method ◽  
Auxiliary Principle ◽  
Auxiliary Principle Technique ◽  
New Class ◽  
Special Cases ◽  
Proof Of Convergence

We introduce and consider a new class of equilibrium problems and variational inequalities involving bifunction, which is called the nonconvex bifunction equilibrium variational inequality. We suggest and analyze some iterative methods for solving the nonconvex bifunction equilibrium variational inequalities using the auxiliary principle technique. We prove that the convergence of implicit method requires only monotonicity. Some special cases are also considered. Our proof of convergence is very simple. Results proved in this paper may stimulate further research in this dynamic field.

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