scholarly journals King-Type Derivative-Free Iterative Families: Real and Memory Dynamics

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-15 ◽  
Author(s):  
F. I. Chicharro ◽  
A. Cordero ◽  
J. R. Torregrosa ◽  
M. P. Vassileva
Keyword(s):  
Quadratic Polynomials ◽  
The Real ◽  
Iterative Schemes ◽  
Derivative Free ◽  
Parametric Plane ◽  
Real Behavior ◽  
Order Four ◽  
Real Stability ◽  
With Memory ◽  
Parametric Class

A biparametric family of derivative-free optimal iterative methods of order four, for solving nonlinear equations, is presented. From the error equation of this class, different families of iterative schemes with memory can be designed increasing the order of convergence up to six. The real stability analysis of the biparametric family without memory is made on quadratic polynomials, finding areas in the parametric plane with good performance. Moreover, in order to study the real behavior of the parametric class with memory, we associate it with a discrete multidimensional dynamical system. By analyzing the fixed and critical points of its vectorial rational function, we can select those methods with best stability properties.

scholarly journals Dynamical Techniques for Analyzing Iterative Schemes with Memory

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-13 ◽  
Author(s):  
Neha Choubey ◽  
A. Cordero ◽  
J. P. Jaiswal ◽  
J. R. Torregrosa
Keyword(s):  
Multidimensional Analysis ◽  
Iterative Schemes ◽  
Derivative Free ◽  
Small Domain ◽  
Hermite Interpolating Polynomial ◽  
Seventh Order ◽  
The Stability ◽  
With Memory ◽  
Theoretical Results ◽  
Made In

We construct a new biparametric three-point method with memory to highly improve the computational efficiency of its original partner, without adding functional evaluations. In this way, through different estimations of self-accelerating parameters, we have modified an existing seventh-order method. The parameters have been defined by Hermite interpolating polynomial that allows the accelerating effect. In particular, the R-order of the proposed iterative method with memory is increased from seven to ten. A real multidimensional analysis of the stability of this method with memory is made, in order to study its dependence on the initial estimations. Taking into account that usually iterative methods with memory are more stable than their derivative-free partners and the obtained results in this study, the behavior of this scheme shows to be excellent, but for a small domain. Numerical examples and comparison are also provided, confirming the theoretical results.

Derivative free iterative methods with memory having higher R-order of convergence

2020 ◽  
Vol 21 (6) ◽  
pp. 641-648
Author(s):  
Pankaj Jain ◽  
Prem Bahadur Chand
Keyword(s):  
Iterative Methods ◽  
Order Of Convergence ◽  
Function Evaluation ◽  
Optimal Methods ◽  
New Methods ◽  
Derivative Free ◽  
Iteration Index ◽  
Order Four ◽  
With Memory ◽  
Theoretical Results

AbstractWe derive two iterative methods with memory for approximating a simple root of any nonlinear equation. For this purpose, we take two optimal methods without memory of order four and eight and convert them into the methods with memory without increasing any further function evaluation. These methods involve a self-accelerator (parameter) that depends upon the iteration index to increase the order of the optimal methods. Consequently, the efficiency of the new methods is considerably high as compared to the methods without memory. Some numerical examples are provided in support of the theoretical results.

Macroeconomic Equilibrium Theory in the Context of Methodological Problems of Contemporary Economic Science

2008 ◽  
pp. 77-88
Author(s):  
M. Likhachev
Keyword(s):  
Empirical Analysis ◽  
Equilibrium States ◽  
Equilibrium Theory ◽  
Economic Systems ◽  
Economic Science ◽  
The Real ◽  
Theoretical Status ◽  
Methodological Problems ◽  
Real Stability

The article is devoted to the analysis of methodological problems in using the conception of macroeconomic equilibrium in contemporary economics. The author considers theoretical status and relevance of equilibrium conception and discusses different areas and limits of applicability of the equilibrium theory. Special attention is paid to different epistemological criteria for this theory taking into account both empirical analysis of the real stability of economic systems and the problem of unobservability of equilibrium states.

scholarly journals Evolving Federations and Regional Public Deficits: Testing the Bailout Hypothesis in the Spanish Case

10.1068/c0444 ◽  
2005 ◽  
Vol 23 (3) ◽  
pp. 437-453 ◽  
Author(s):  
Santiago Lago-Peñas
Keyword(s):  
Financial Markets ◽  
Empirical Research ◽  
Central Government ◽  
Traditional Model ◽  
Factors Affecting ◽  
The Real ◽  
Government Deficits ◽  
Tax Autonomy ◽  
Real Behavior ◽  
Public Deficits

High debt autonomy and low tax autonomy often characterize evolving federations, making the bailout hypothesis very attractive in resolving subcentral government deficits. However, meeting both conditions is not enough to conclude that bailout expectations are the main reason for a potential deficit. There are many other factors affecting expectations and the real behavior of the agents involved: central government, subcentral governments, and the financial markets. Empirical research is the only means by which to determine the relevance of the bailout problem in each situation. To demonstrate this argument, the author describes an exhaustive analysis of the Spanish case. The main conclusion is that deficit seems to be better understood by a more traditional model of fiscal choices than by bailout expectations.

scholarly journals Reversals in the large-scale αΩ-dynamo with memory

2015 ◽  
Vol 22 (4) ◽  
pp. 361-369 ◽  
Author(s):  
L. K. Feschenko ◽  
G. M. Vodinchar
Keyword(s):  
Magnetic Field ◽  
Power Law ◽  
Geomagnetic Field ◽  
Large Scale ◽  
Magnetic Polarity ◽  
Power Law Model ◽  
The Real ◽  
Geomagnetic Polarity ◽  
With Memory ◽  
The Magnetic Field

Abstract. Inversion of the magnetic field in a model of large-scale αΩ-dynamo with α-effect with stochastic memory is under investigation. The model allows us to reproduce the main features of the geomagnetic field reversals. It was established that the polarity intervals in the model are distributed according to the power law. Model magnetic polarity timescale is fractal. Its dimension is consistent with the dimension of the real geomagnetic polarity timescale.

scholarly journals On a Derivative-Free Variant of King’s Family with Memory

2015 ◽  
Vol 2015 ◽  
pp. 1-5
Author(s):  
M. Sharifi ◽  
S. Karimi Vanani ◽  
F. Khaksar Haghani ◽  
M. Arab ◽  
S. Shateyi
Keyword(s):  
Nonlinear Equations ◽  
Numerical Experiments ◽  
Order Of Convergence ◽  
Derivative Free ◽  
With Memory

The aim of this paper is to construct a method with memory according to King’s family of methods without memory for nonlinear equations. It is proved that the proposed method possesses higherR-order of convergence using the same number of functional evaluations as King’s family. Numerical experiments are given to illustrate the performance of the constructed scheme.

scholarly journals Efficient Four-Parametric with-and-without-Memory Iterative Methods Possessing High Efficiency Indices

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Alicia Cordero ◽  
Moin-ud-Din Junjua ◽  
Juan R. Torregrosa ◽  
Nusrat Yasmin ◽  
Fiza Zafar
Keyword(s):  
Iterative Methods ◽  
High Efficiency ◽  
Nonlinear Function ◽  
Efficiency Index ◽  
Simple Zero ◽  
Eighth Order ◽  
New Family ◽  
Derivative Free ◽  
With Memory ◽  
Theoretical Results

We construct a family of derivative-free optimal iterative methods without memory to approximate a simple zero of a nonlinear function. Error analysis demonstrates that the without-memory class has eighth-order convergence and is extendable to with-memory class. The extension of new family to the with-memory one is also presented which attains the convergence order 15.5156 and a very high efficiency index 15.51561/4≈1.9847. Some particular schemes of the with-memory family are also described. Numerical examples and some dynamical aspects of the new schemes are given to support theoretical results.

scholarly journals Impact on Stability by the Use of Memory in Traub-Type Schemes

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 274
Author(s):  
Francisco I. Chicharro ◽  
Alicia Cordero ◽  
Neus Garrido ◽  
Juan R. Torregrosa
Keyword(s):  
Order Of Convergence ◽  
Nonlinear Problems ◽  
Higher Order ◽  
Lower Number ◽  
Dynamical Analysis ◽  
The Real ◽  
Original Scheme ◽  
Interpolation Polynomials ◽  
With Memory ◽  
Number Of Iterations

In this work, two Traub-type methods with memory are introduced using accelerating parameters. To obtain schemes with memory, after the inclusion of these parameters in Traub’s method, they have been designed using linear approximations or the Newton’s interpolation polynomials. In both cases, the parameters use information from the current and the previous iterations, so they define a method with memory. Moreover, they achieve higher order of convergence than Traub’s scheme without any additional functional evaluations. The real dynamical analysis verifies that the proposed methods with memory not only converge faster, but they are also more stable than the original scheme. The methods selected by means of this analysis can be applied for solving nonlinear problems with a wider set of initial estimations than their original partners. This fact also involves a lower number of iterations in the process.

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