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Ioannis K Argyros - One of the best experts on this subject based on the ideXlab platform.

  • on the complexity of extending the Convergence Ball of wang s method for finding a zero of a derivative
    Journal of Complexity, 2021
    Co-Authors: Hongmin Ren, Ioannis K Argyros
    Abstract:

    Abstract Ball Convergence results are very important, since they demonstrate the complexity in choosing initial points for iterative methods. One of the most important problems in the study of iterative methods is to determine the Convergence Ball. This Ball is small in general restricting the choice of initial points. We address this problem in the case of Wang’s method utilized to determine a zero of a derivative. Finding such a zero has many applications in computational fields, especially in function optimization. In particular, we find the Convergence Ball of Wang’s method using hypotheses up to the second derivative in contrast to earlier studies using hypotheses up to the fourth derivative. This way, we also extend the applicability of Wang’s method. Numerical experiments used to test the Convergence criteria complete this study.

  • Extending the Applicability of Newton’s Algorithm with Projections for Solving Generalized Equations
    Applied System Innovation, 2020
    Co-Authors: Michael Argyros, Ioannis K Argyros, Gus Argyros, Samundra Regmi, Santhosh George
    Abstract:

    A new technique is developed to extend the Convergence Ball of Newton’s algorithm with projections for solving generalized equations with constraints on the multidimensional Euclidean space. This goal is achieved by locating a more precise region than in earlier studies containing the solution on which the Lipschitz constants are smaller than the ones used in previous studies. These advances are obtained without additional conditions. This technique can be used to extend the usage of other iterative algorithms. Numerical experiments are used to demonstrate the superiority of the new results.

  • Convergence Ball and complex geometry of an iteration function of higher order
    Mathematics, 2018
    Co-Authors: Deepak Kumar, Ioannis K Argyros, Janak Raj Sharma
    Abstract:

    Higher-order derivatives are used to determine the Convergence order of iterative methods. However, such derivatives are not present in the formulas. Therefore, the assumptions on the higher-order derivatives of the function restrict the applicability of methods. Our Convergence analysis of an eighth-order method uses only the derivative of order one. The Convergence results so obtained are applied to some real problems, which arise in science and engineering. Finally, stability of the method is checked through complex geometry shown by drawing basins of attraction of the solutions.

  • Local Convergence of Jarratt-Type Methods with Less Computation of Inversion Under Weak Conditions
    Mathematical Modelling and Analysis, 2017
    Co-Authors: Ioannis K Argyros, Santhosh George
    Abstract:

    AbstractWe present a local Convergence analysis for Jarratt-type methods in order to approximate a solution of a nonlinear equation in a Banach space setting. Earlier studies cannot be used to solve equations using such methods. The Convergence Ball and error estimates are given for these methods. Numerical examples are also provided in this study.

  • Local Convergence of deformed Euler–Halley-type methods in Banach space under weak conditions
    Asian-european Journal of Mathematics, 2017
    Co-Authors: Ioannis K Argyros, Santhosh George
    Abstract:

    We present a unified local Convergence analysis for deformed Euler–Halley-type methods in order to approximate a solution of a nonlinear equation in a Banach space setting. Our methods include the Euler, Halley and other high order methods. The Convergence Ball and error estimates are given for these methods under hypotheses up to the first Frechet derivative in contrast to earlier studies using hypotheses up to the second Frechet derivative. Numerical examples are also provided in this study.

Jigui Jian - One of the best experts on this subject based on the ideXlab platform.

  • Global exponential Convergence for impulsive inertial complex-valued neural networks with time-varying delays
    Mathematics and Computers in Simulation, 2019
    Co-Authors: Qian Tang, Jigui Jian
    Abstract:

    Abstract This paper focuses on the exponential Convergence of impulsive inertial complex-valued neural networks with time-varying delays. The system can be expressed as a first order differential equation by selecting a proper variable substitution. By constructing proper Lyapunov–Krasovskii functionals and using inequality techniques, some delay-dependent sufficient conditions in linear matrix inequality form are proposed to ascertain the global exponential Convergence of the addressed neural networks with two classes of complex-valued activation functions. The framework of the exponential Convergence Ball domain in which all trajectories converge is also given. Meanwhile, the obtained results here do not meet that the derivatives of the time-varying delays are less than one and there are also no limit to the strength of impulses. The methods here can also be applied to deal with multistable and monostable neural networks because of making no hypotheses on the amount of the equilibrium points. Finally, two examples are given to demonstrate the validity of the theoretical results.

  • Global exponential Convergence of fuzzy complex-valued neural networks with time-varying delays and impulsive effects
    Fuzzy Sets and Systems, 2018
    Co-Authors: Jigui Jian, Peng Wan
    Abstract:

    Abstract In this paper, the global exponential Convergence of T–S fuzzy complex-valued neural networks with time-varying delays and impulsive effects is discussed. By employing Lyapunov functional method and matrix inequality technique, we analyze a type of activation functions with Lipschitz function, and sufficient conditions in terms of complex-valued linear matrix inequality are obtained to ensure the global exponential Convergence. Moreover, the framework of the exponential Convergence Ball in the state space of the considered neural networks and the exponential Convergence rate index are also given out. Here, the existence and uniqueness of the equilibrium points need not be considered and the results improve existing results on the Lyapunov exponential stability as special cases. Finally, one numerical example with simulations is given to illustrate the effectiveness of our theoretical results.

  • Lagrange -exponential stability and -exponential Convergence for fractional-order complex-valued neural networks
    Neural networks : the official journal of the International Neural Network Society, 2017
    Co-Authors: Jigui Jian, Peng Wan
    Abstract:

    This paper deals with the problem on Lagrange -exponential stability and -exponential Convergence for a class of fractional-order complex-valued neural networks. To this end, some new fractional-order differential inequalities are established, which improve and generalize previously known criteria. By using the new inequalities and coupling with the Lyapunov method, some effective criteria are derived to guarantee Lagrange -exponential stability and -exponential Convergence of the addressed network. Moreover, the framework of the -exponential Convergence Ball is also given, where the Convergence rate is related to the parameters and the order of differential of the system. These results here, which the existence and uniqueness of the equilibrium points need not to be considered, generalize and improve the earlier publications and can be applied to monostable and multistable fractional-order complex-valued neural networks. Finally, one example with numerical simulations is given to show the effectiveness of the obtained results.

  • Global Convergence analysis of impulsive inertial neural networks with time-varying delays
    Neurocomputing, 2017
    Co-Authors: Peng Wan, Jigui Jian
    Abstract:

    In this paper, a class of impulsive inertial neural networks with time-varying delays is considered. By choosing proper variable transformation, the original inertial neural networks can be rewritten as first-order differential equations. Based on Lyapunov functions method and inequality techniques, some sufficient conditions are derived to guarantee global exponential Convergence of the discussed inertial neural networks with impulsive effects. Meanwhile, the framework of the exponential Convergence Ball in the state space with a pre-specified Convergence rate is also given. Here, the existence and uniqueness of the equilibrium points need not to be considered. Finally, some numerical examples with simulation are presented to show the effectiveness of the obtained results.

  • exponential Convergence and lagrange stability for impulsive cohen grossberg neural networks with time varying delays
    Journal of Computational and Applied Mathematics, 2015
    Co-Authors: Liangliang Li, Jigui Jian
    Abstract:

    In this paper, the problem on exponential Convergence and Lagrange exponential stability for a class of delayed Cohen-Grossberg neural networks with impulses effects is investigated. To this end, a new delay impulsive differential inequality is established, which improves and generalizes previously known criteria. By using the new inequality and coupling with the Lyapunov method, several sufficient conditions are derived to guarantee the global exponential stability in Lagrange sense and exponential Convergence of the state variables of the discussed delayed Cohen-Grossberg neural networks with impulses effects. Meanwhile, the framework of the exponential Convergence Ball in the state space with a pre-specified Convergence rate is also given. Here, the existence and uniqueness of the equilibrium points need not to be considered. Finally, some numerical examples with simulation show the effectiveness of the obtained results. We discuss Lagrange stability for impulsive Cohen-Grossberg neural networks.We establish a new delay impulsive differential inequality.Some easily verified conditions of Lagrange exponential stability are obtained.Giving out the detail estimations of the exponential Convergence Ball.The results here generalize and improve the earlier publications.

Peng Wan - One of the best experts on this subject based on the ideXlab platform.

  • Global exponential Convergence of fuzzy complex-valued neural networks with time-varying delays and impulsive effects
    Fuzzy Sets and Systems, 2018
    Co-Authors: Jigui Jian, Peng Wan
    Abstract:

    Abstract In this paper, the global exponential Convergence of T–S fuzzy complex-valued neural networks with time-varying delays and impulsive effects is discussed. By employing Lyapunov functional method and matrix inequality technique, we analyze a type of activation functions with Lipschitz function, and sufficient conditions in terms of complex-valued linear matrix inequality are obtained to ensure the global exponential Convergence. Moreover, the framework of the exponential Convergence Ball in the state space of the considered neural networks and the exponential Convergence rate index are also given out. Here, the existence and uniqueness of the equilibrium points need not be considered and the results improve existing results on the Lyapunov exponential stability as special cases. Finally, one numerical example with simulations is given to illustrate the effectiveness of our theoretical results.

  • Lagrange -exponential stability and -exponential Convergence for fractional-order complex-valued neural networks
    Neural networks : the official journal of the International Neural Network Society, 2017
    Co-Authors: Jigui Jian, Peng Wan
    Abstract:

    This paper deals with the problem on Lagrange -exponential stability and -exponential Convergence for a class of fractional-order complex-valued neural networks. To this end, some new fractional-order differential inequalities are established, which improve and generalize previously known criteria. By using the new inequalities and coupling with the Lyapunov method, some effective criteria are derived to guarantee Lagrange -exponential stability and -exponential Convergence of the addressed network. Moreover, the framework of the -exponential Convergence Ball is also given, where the Convergence rate is related to the parameters and the order of differential of the system. These results here, which the existence and uniqueness of the equilibrium points need not to be considered, generalize and improve the earlier publications and can be applied to monostable and multistable fractional-order complex-valued neural networks. Finally, one example with numerical simulations is given to show the effectiveness of the obtained results.

  • Global Convergence analysis of impulsive inertial neural networks with time-varying delays
    Neurocomputing, 2017
    Co-Authors: Peng Wan, Jigui Jian
    Abstract:

    In this paper, a class of impulsive inertial neural networks with time-varying delays is considered. By choosing proper variable transformation, the original inertial neural networks can be rewritten as first-order differential equations. Based on Lyapunov functions method and inequality techniques, some sufficient conditions are derived to guarantee global exponential Convergence of the discussed inertial neural networks with impulsive effects. Meanwhile, the framework of the exponential Convergence Ball in the state space with a pre-specified Convergence rate is also given. Here, the existence and uniqueness of the equilibrium points need not to be considered. Finally, some numerical examples with simulation are presented to show the effectiveness of the obtained results.

Santhosh George - One of the best experts on this subject based on the ideXlab platform.

  • Extending the Applicability of Newton’s Algorithm with Projections for Solving Generalized Equations
    Applied System Innovation, 2020
    Co-Authors: Michael Argyros, Ioannis K Argyros, Gus Argyros, Samundra Regmi, Santhosh George
    Abstract:

    A new technique is developed to extend the Convergence Ball of Newton’s algorithm with projections for solving generalized equations with constraints on the multidimensional Euclidean space. This goal is achieved by locating a more precise region than in earlier studies containing the solution on which the Lipschitz constants are smaller than the ones used in previous studies. These advances are obtained without additional conditions. This technique can be used to extend the usage of other iterative algorithms. Numerical experiments are used to demonstrate the superiority of the new results.

  • Extended local Convergence analysis of inexact Gauss-Newton method for singular systems of equations under weak conditions
    Studia Universitatis Babes-Bolyai Matematica, 2017
    Co-Authors: Santhosh George
    Abstract:

    A new semi-local Convergence analysis of the Gauss-Newton method for solving convex composite optimization problems is presented using restricted Convergence domains.  The results extend the applicability of the Gauss-Newton method under the same computational cost as in earlier studies. In particular, the advantages are: the error estimates on the distances involved are tighter and the Convergence Ball is at least as large. Moreover, the majorant function in contrast to earlier studies is not necessarily differentiable.   Numerical examples are also provided in this study.

  • Local Convergence of Jarratt-Type Methods with Less Computation of Inversion Under Weak Conditions
    Mathematical Modelling and Analysis, 2017
    Co-Authors: Ioannis K Argyros, Santhosh George
    Abstract:

    AbstractWe present a local Convergence analysis for Jarratt-type methods in order to approximate a solution of a nonlinear equation in a Banach space setting. Earlier studies cannot be used to solve equations using such methods. The Convergence Ball and error estimates are given for these methods. Numerical examples are also provided in this study.

  • local Convergence of deformed euler halley type methods in banach space under weak conditions
    Asian-european Journal of Mathematics, 2017
    Co-Authors: Ioannis K Argyros, Santhosh George
    Abstract:

    We present a unified local Convergence analysis for deformed Euler–Halley-type methods in order to approximate a solution of a nonlinear equation in a Banach space setting. Our methods include the Euler, Halley and other high order methods. The Convergence Ball and error estimates are given for these methods under hypotheses up to the first Frechet derivative in contrast to earlier studies using hypotheses up to the second Frechet derivative. Numerical examples are also provided in this study.

  • Local Convergence of deformed Euler–Halley-type methods in Banach space under weak conditions
    Asian-European Journal of Mathematics, 2017
    Co-Authors: Ioannis K Argyros, Santhosh George
    Abstract:

    We present a unified local Convergence analysis for deformed Euler–Halley-type methods in order to approximate a solution of a nonlinear equation in a Banach space setting. Our methods include the Euler, Halley and other high order methods. The Convergence Ball and error estimates are given for these methods under hypotheses up to the first Fréchet derivative in contrast to earlier studies using hypotheses up to the second Fréchet derivative. Numerical examples are also provided in this study.

Hongmin Ren - One of the best experts on this subject based on the ideXlab platform.

  • on the complexity of extending the Convergence Ball of wang s method for finding a zero of a derivative
    Journal of Complexity, 2021
    Co-Authors: Hongmin Ren, Ioannis K Argyros
    Abstract:

    Abstract Ball Convergence results are very important, since they demonstrate the complexity in choosing initial points for iterative methods. One of the most important problems in the study of iterative methods is to determine the Convergence Ball. This Ball is small in general restricting the choice of initial points. We address this problem in the case of Wang’s method utilized to determine a zero of a derivative. Finding such a zero has many applications in computational fields, especially in function optimization. In particular, we find the Convergence Ball of Wang’s method using hypotheses up to the second derivative in contrast to earlier studies using hypotheses up to the fourth derivative. This way, we also extend the applicability of Wang’s method. Numerical experiments used to test the Convergence criteria complete this study.

  • Convergence Analysis of the Modified Chebyshev’s Method for Finding Multiple Roots
    Vietnam Journal of Mathematics, 2021
    Co-Authors: Rongfei Lin, Hongmin Ren, Yasir Khan
    Abstract:

    In this paper, an estimate of the radius of Convergence Ball of the modified Chebyshev’s method for finding multiple roots of nonlinear equations is provided under the hypotheses that the (m + 1)st derivative f(m+ 1) of function f is Holder continuous and bounded. The unique Ball of a solution is also established. Finally, some examples are provided to show the effectiveness of our results.

  • Local Convergence of efficient Secant-type methods for solving nonlinear equations
    Applied Mathematics and Computation, 2012
    Co-Authors: Hongmin Ren, Ioannis K Argyros
    Abstract:

    Abstract A local Convergence analysis for an efficient Secant-type method (STM) for solving nonlinear equations is given using both the Lipschitz continuous and center-Lipshchitz continuous divided differences of order one. An estimate of the radius of the Convergence Ball of (STM) is provided, the error estimate matching its Convergence order is established. Numerical examples validating the theoretical results are also provided in the concluding section of this study.

  • Convergence of the modified Halley's method for multiple zeros under Hölder continuous derivative
    Numerical Algorithms, 2011
    Co-Authors: Hongmin Ren
    Abstract:

    In this paper, the estimate of the radius of the Convergence Ball of the modified Halley's method for finding multiple zeros of nonlinear equations is provided under the hypotheses that the derivative f (m?+?1) of function f is Holder continuous, and f (m?+?1) is bounded. The uniqueness Ball of solution is also established. Finally, some examples are provided to show applications of our theorem.

  • Convergence Ball and error analysis of Ostrowski-Traub's method
    Applied Mathematics-A Journal of Chinese Universities, 2010
    Co-Authors: Hongmin Ren
    Abstract:

    Under the hypotheses that the second-order and third-order derivatives of a function are bounded, an estimate of the radius of the Convergence Ball of Ostrowski-Traub’s method is obtained. An error analysis is given which matches the Convergence order of the method. Finally, two examples are provided to show applications of our theorem.