Efficient Sixth Convergence Order Method

2021 ◽  
pp. 161-174
Author(s):  
Ioannis K. Argyros
Keyword(s):  
Convergence Order ◽  
Order Method

scholarly journals Local Convergence of an Efficient High Convergence Order Method Using Hypothesis Only on the First Derivative

Algorithms ◽  
2015 ◽  
Vol 8 (4) ◽  
pp. 1076-1087 ◽  
Author(s):  
Ioannis Argyros ◽  
Ramandeep Behl ◽  
S.S. Motsa
Keyword(s):  
Local Convergence ◽  
Convergence Order ◽  
Order Method ◽  
First Derivative

scholarly journals Convergence Analysis of a Three Step Newton-like Method for Nonlinear Equations in Banach Space under Weak Conditions

2016 ◽  
Vol 54 (2) ◽  
pp. 37-46
Author(s):  
Ioannis K. Argyros ◽  
Santhosh George
Keyword(s):  
Banach Space ◽  
Convergence Analysis ◽  
Nonlinear Equations ◽  
Local Convergence ◽  
Convergence Order ◽  
Order Method ◽  
Numerical Examples ◽  
Local Convergence Analysis

Abstract In the present paper, we study the local convergence analysis of a fifth convergence order method considered by Sharma and Guha in [15] to solve equations in Banach space. Using our idea of restricted convergence domains we extend the applicability of this method. Numerical examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.

A Modified Newton–Özban Composition for Solving Nonlinear Systems

2019 ◽  
Vol 17 (08) ◽  
pp. 1950047
Author(s):  
Rajni Sharma ◽  
Janak Raj Sharma ◽  
Nitin Kalra
Keyword(s):  
Nonlinear Systems ◽  
Computational Efficiency ◽  
Basins Of Attraction ◽  
Convergence Order ◽  
Order Method ◽  
Third Order ◽  
Numerical Examples ◽  
Scalar Equations ◽  
Appl Math ◽  
Methods Numerical

In this work, a modified Newton–Özban composition of convergence order six for solving nonlinear systems is presented. The first two steps of proposed scheme are based on third-order method given by Özban [Özban, A. Y. [2004] “Some new variants of Newton’s method,” Appl. Math. Lett. 17, 677–682.] for solving scalar equations. Computational efficiency of the presented method is discussed and compared with well-known existing methods. Numerical examples are studied to demonstrate the accuracy of the proposed method. The basins of attraction of some of the existing methods along with the proposed method are given to exhibit their performance.

Routing Optimization with Efficient Second Order Distributed Approach Using Congestion Control Rules

2017 ◽  
Vol 7 (7) ◽  
pp. 363
Author(s):  
Jaya Pratha Sebastiyar ◽  
Martin Sahayaraj Joseph
Keyword(s):  
Congestion Control ◽  
Second Order ◽  
Back Pressure ◽  
Order Method ◽  
Delay Performance ◽  
Routing Optimization ◽  
Distributed Approach ◽  
Control Rules ◽  
Primal Dual ◽  
Queue Stability

Distributed joint congestion control and routing optimization has received a significant amount of attention recently. To date, however, most of the existing schemes follow a key idea called the back-pressure algorithm. Despite having many salient features, the first-order sub gradient nature of the back-pressure based schemes results in slow convergence and poor delay performance. To overcome these limitations, the present study was made as first attempt at developing a second-order joint congestion control and routing optimization framework that offers utility-optimality, queue-stability, fast convergence, and low delay.  Contributions in this project are three-fold. The present study propose a new second-order joint congestion control and routing framework based on a primal-dual interior-point approach and established utility-optimality and queue-stability of the proposed second-order method. The results of present study showed that how to implement the proposed second-order method in a distributed fashion.

scholarly journals Superconvergence of interpolated collocation solutions for weakly singular Volterra integral equations of the second kind

2021 ◽  
Vol 40 (3) ◽  
Author(s):  
Qiumei Huang ◽  
Min Wang
Keyword(s):  
Integral Equations ◽  
Numerical Experiments ◽  
Volterra Integral Equations ◽  
Least Square ◽  
Convergence Order ◽  
Collocation Points ◽  
Weakly Singular ◽  
Interpolation Postprocessing ◽  
Collocation Solution

AbstractIn this paper, we discuss the superconvergence of the “interpolated” collocation solutions for weakly singular Volterra integral equations of the second kind. Based on the collocation solution $$u_h$$ u h , two different interpolation postprocessing approximations of higher accuracy: $$I_{2h}^{2m-1}u_h$$ I 2 h 2 m - 1 u h based on the collocation points and $$I_{2h}^{m}u_h$$ I 2 h m u h based on the least square scheme are constructed, whose convergence order are the same as that of the iterated collocation solution. Such interpolation postprocessing methods are much simpler in computation. We further apply this interpolation postprocessing technique to hybrid collocation solutions and similar results are obtained. Numerical experiments are shown to demonstrate the efficiency of the interpolation postprocessing methods.

Stabilization for a class of delayed switched inertial neural networks via non-reduced order method

2021 ◽  
pp. 014233122098594
Author(s):  
Xuan Chen ◽  
Dongyun Lin
Keyword(s):  
Neural Networks ◽  
Comparative Research ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Global Stabilization ◽  
Order Method ◽  
Reduced Order ◽  
Global Asymptotic Stabilization ◽  
Inertial Neural Networks ◽  
Barbalat Lemma

This paper tackles the issue of global stabilization for a class of delayed switched inertial neural networks (SINN). Distinct from the frequently employed reduced-order technique, this paper studies SINN directly through non-reduced order method. By constructing a novel Lyapunov functional and using Barbalat Lemma, sufficient conditions for the global asymptotic stabilization issue and global exponential stabilization issue of the considered SINN are established. Numerical simulations further confirm the feasibility of the main results. The comparative research shows that global stabilization results of this paper complement and improve some existing work.

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