The Experts below are selected from a list of 26619 Experts worldwide ranked by ideXlab platform
Ioannis K Argyros - One of the best experts on this subject based on the ideXlab platform.
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On an iterative method without inverses of derivatives for solving equations
Advances in the Theory of Nonlinear Analysis and its Application, 2020Co-Authors: Santhosh George, Ioannis K ArgyrosAbstract:We present the semi-Local Convergence Analysis of a Potra-type method to solve equations involving Banach space valued operators. The Analysis is based on our ideas of recurrent functions and restricted Convergence region. The study is completed using numerical examples.
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an optimal reconstruction of chebyshev halley type methods with Local Convergence Analysis
International Journal of Computational Methods, 2020Co-Authors: Ali Saleh Alshomrani, Ioannis K Argyros, Ramandeep BehlAbstract:Our principle aim in this paper is to present a new reconstruction of classical Chebyshev–Halley schemes having optimal fourth and eighth-order of Convergence for all parameters α unlike in the ear...
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High Convergence Order Q-Step Methods for Solving Equations and Systems of Equations
Contemporary Mathematics, 2020Co-Authors: Ioannis K Argyros, Santhosh GeorgeAbstract:The Local Convergence Analysis of iterative methods is important since it demonstrates the degree of diffculty for choosing initial points. In the present study, we introduce generalized multi-step high order methods for solving nonlinear equations. The Local Convergence Analysis is given using hypotheses only on the first derivative which actually appears in the methods in contrast to earlier works using hypotheses on higher order derivatives. This way we extend the applicability of these methods. The Analysis includes computable radius of Convergence as well as error bounds based on Lipschitz-type conditions not given in earlier studies. Numerical examples conclude this study.
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Newton-Type Solvers Using Outer Inverses for Singular Equations
Games and Dynamics in Economics, 2020Co-Authors: Ioannis K Argyros, Stepan ShakhnoAbstract:We are motivated by a seminal paper of Nashed and Chen on Newton-type solvers for Banach space valued operators equations. The novelty of our paper lies in the fact that we present a more flexible, finer semi-Local Convergence Analysis and without additional hypotheses. We also study the Local Convergence Analysis not given in the aforementioned paper.
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Ball Convergence for a Multi-Step Harmonic Mean Newton-Like Method in Banach Space
International Journal of Computational Methods, 2019Co-Authors: Ramandeep Behl, Ali Saleh Alshormani, Ioannis K ArgyrosAbstract:In this paper, we present a Local Convergence Analysis of some iterative methods to approximate a Locally unique solution of nonlinear equations in a Banach space setting. In the earlier study [Bab...
Saïd Hilout - One of the best experts on this subject based on the ideXlab platform.
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Robust semi-Local Convergence Analysis for inexact Newton method
Applied Mathematics and Computation, 2014Co-Authors: Ioannis K Argyros, Saïd Hilout, Á. Alberto MagreñánAbstract:We present a more flexible semi-Local Convergence Analysis for inexact Newton with relative residual error tolerance than in earlier studies. A combination of a majorant function and a center-majorant function is used in the Convergence Analysis. The center-majorant function is used instead of the majorant function to obtain more precise estimates. The advantages of the new approach are under the same computational cost: weaker Convergence criteria; more precise error estimates on the distances involved and an at least as precise information on the location of the solution. Special cases and applications are also provided in the study.
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improved Local Convergence Analysis of inexact gauss newton like methods under the majorant condition in banach spaces
Journal of The Franklin Institute-engineering and Applied Mathematics, 2013Co-Authors: Ioannis K Argyros, Saïd HiloutAbstract:Abstract We present a Local Convergence Analysis of inexact Gauss–Newton like methods for solving nonlinear equations in a Banach space setting. Using more precise majorant conditions than in earlier studies, we provide a larger radius of Convergence; tighter error estimates on the distances involved and a clearer relationship between the majorant function and the associated least squares problem. Moreover, these advantages are obtained under the same computational cost.
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Improved Local Convergence Analysis of inexact Gauss–Newton like methods under the majorant condition in Banach spaces
Journal of the Franklin Institute, 2013Co-Authors: Ioannis K Argyros, Saïd HiloutAbstract:Abstract We present a Local Convergence Analysis of inexact Gauss–Newton like methods for solving nonlinear equations in a Banach space setting. Using more precise majorant conditions than in earlier studies, we provide a larger radius of Convergence; tighter error estimates on the distances involved and a clearer relationship between the majorant function and the associated least squares problem. Moreover, these advantages are obtained under the same computational cost.
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Improved Local Convergence of Newton's method under weak majorant condition
Journal of Computational and Applied Mathematics, 2012Co-Authors: Ioannis K Argyros, Saïd HiloutAbstract:We provide a Local Convergence Analysis for Newton's method under a weak majorant condition in a Banach space setting. Our results provide under the same information a larger radius of Convergence and tighter error estimates on the distances involved than before [14]. Special cases and numerical examples are also provided in this study.
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an improved Local Convergence Analysis for newton steffensen type method
Journal of Applied Mathematics and Computing, 2010Co-Authors: Ioannis K Argyros, Saïd HiloutAbstract:We provide a Local Convergence Analysis for Newton–Steffensen-type algorithm for solving nonsmooth perturbed variational inclusions in Banach spaces. Under new center–conditions and the Aubin continuity property, we obtain the linear Local Convergence of Newton–Steffensen method. Our results compare favorably with related obtained in (Argyros and Hilout, 2007 submitted; Hilout in J. Math. Anal. Appl. 339:753–761, 2008).
Santhosh George - One of the best experts on this subject based on the ideXlab platform.
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On an iterative method without inverses of derivatives for solving equations
Advances in the Theory of Nonlinear Analysis and its Application, 2020Co-Authors: Santhosh George, Ioannis K ArgyrosAbstract:We present the semi-Local Convergence Analysis of a Potra-type method to solve equations involving Banach space valued operators. The Analysis is based on our ideas of recurrent functions and restricted Convergence region. The study is completed using numerical examples.
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High Convergence Order Q-Step Methods for Solving Equations and Systems of Equations
Contemporary Mathematics, 2020Co-Authors: Ioannis K Argyros, Santhosh GeorgeAbstract:The Local Convergence Analysis of iterative methods is important since it demonstrates the degree of diffculty for choosing initial points. In the present study, we introduce generalized multi-step high order methods for solving nonlinear equations. The Local Convergence Analysis is given using hypotheses only on the first derivative which actually appears in the methods in contrast to earlier works using hypotheses on higher order derivatives. This way we extend the applicability of these methods. The Analysis includes computable radius of Convergence as well as error bounds based on Lipschitz-type conditions not given in earlier studies. Numerical examples conclude this study.
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Local Convergence Analysis of two competing two-step iterative methods free of derivatives for solving equations and systems of equations
Mathematical Communications, 2019Co-Authors: Ioannis K Argyros, Santhosh GeorgeAbstract:We present the Local Convergence Analysis of two-step iterative methods free of derivatives for solving equations and systems of equations under similar hypotheses based on Lipschitz-type conditions. The methods are in particular useful for solving equations or systems involving non-differentiable terms. A comparison is also provided using suitable numerical examples.
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Extending the Applicability of a Newton-Kurchatov-Type Method for Solving Non-Differentiable Equations in Banach Spaces
Communications in Advanced Mathematical Sciences, 2019Co-Authors: Ioannis K Argyros, Santhosh GeorgeAbstract:We provide a new Local Convergence Analysis of a Newton-Kurchatov-like method to solve non-differentiable equations in Banach spaces. Our result improve the earlier works in literature. The examples were used to test our hypotheses.
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On a Two-Step Kurchatov-Type Method in Banach Space
Mediterranean Journal of Mathematics, 2019Co-Authors: Ioannis K Argyros, Santhosh GeorgeAbstract:We present the semi-Local Convergence Analysis of a two-step Kurchatov-type method to solve equations involving Banach space valued operators. The Analysis is based on our ideas of recurrent functions and restricted Convergence region. The study is completed using numerical examples.
Á. Alberto Magreñán - One of the best experts on this subject based on the ideXlab platform.
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Different methods for solving STEM problems
Journal of Mathematical Chemistry, 2019Co-Authors: Ioannis K Argyros, Á. Alberto Magreñán, L. Orcos, Íñígo Sarría, Juan Antonio SiciliaAbstract:We first present a Local Convergence Analysis for some families of fourth and six order methods in order to approximate a Locally unique solution of a nonlinear equation in a Banach space setting. Earlier studies have used hypotheses on the fourth Fréchet-derivative of the operator involved. We use hypotheses only on the first Fréchet-derivative in one Local Convergence Analysis. This way, the applicability of these methods is extended. Moreover, the radius of Convergence and computable error bounds on the distances involved are also given in this study based on Lipschitz constants. Numerical examples illustrating the theoretical results are also presented in this study.
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Improved semi-Local Convergence of the Newton-HSS method for solving large systems of equations
Applied Mathematics Letters, 2019Co-Authors: Ioannis K Argyros, Santhosh George, Á. Alberto MagreñánAbstract:Abstract The aim of this article is to present the correct version of the main theorem 3.2 given in Guo and Duff (2011), concerning the semi-Local Convergence Analysis of the Newton-HSS (NHSS) method for solving systems of nonlinear equations. Our Analysis also includes the corrected upper bound on the initial point.
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Gauss–Newton method
A Contemporary Study of Iterative Methods, 2018Co-Authors: Á. Alberto Magreñán, Ioannis K ArgyrosAbstract:In this chapter we present the Local Convergence Analysis of Gauss–Newton method using the idea of restricted Convergence domains, which allows us to improve previous results. Finally, some special cases and a numerical example are also given, validating the theoretical results.
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Local Convergence and the Dynamics of a Two-Step Newton-Like Method
International Journal of Bifurcation and Chaos, 2016Co-Authors: Ioannis K Argyros, Á. Alberto MagreñánAbstract:We present the Local Convergence Analysis and the study of the dynamics of a two-step Newton-like method in order to approximate a Locally unique solution of multiplicity one of a nonlinear equation.
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new semiLocal and Local Convergence Analysis for the secant method
Applied Mathematics and Computation, 2015Co-Authors: Á. Alberto Magreñán, Ioannis K ArgyrosAbstract:We present a new Convergence Analysis, for the Secant method in order to approximate a Locally unique solution of a nonlinear equation in a Banach space. Our idea uses Lipschitz and center-Lipschitz instead of just Lipschitz conditions in the Convergence Analysis. The new Convergence Analysis leads to more precise error bounds and to a better information on the location of the solution than the corresponding ones in earlier studies such as 2,6,9,11,14,15,17,20,22-26]. Numerical examples validating the theoretical results are also provided in this study.
George A Anastassiou - One of the best experts on this subject based on the ideXlab platform.
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Generalized iterative procedures and their applications to Banach space valued functions in abstract fractional calculus
SeMA Journal, 2018Co-Authors: George A Anastassiou, Ioannis K ArgyrosAbstract:The objective in this study is to use generalized iterative procedures in order to approximate solutions of an equation on a Banach space setting. In particular, we present a semi-Local Convergence Analysis for these methods. Some applications are suggested including Banach space valued functions of fractional calculus, where all integrals are of Bochner-type.
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Iterative Convergence with Banach Space Valued Functions in Abstract Fractional Calculus
Annals of the West University of Timisoara: Mathematics and Computer Science, 2017Co-Authors: George A Anastassiou, Ioannis K ArgyrosAbstract:AbstractThe goal of this paper is to present a semi-Local Convergence Analysis for some iterative methods under generalized conditions. The operator is only assumed to be continuous and its domain is open. Applications are suggested including Banach space valued functions of fractional calculus, where all integrals are of Bochner-type.
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Semi-Local Convergence in Right Abstract Fractional Calculus
Functional Numerical Methods: Applications to Abstract Fractional Calculus, 2017Co-Authors: George A Anastassiou, Ioannis K ArgyrosAbstract:We provide a semi-Local Convergence Analysis for a class of iterative methods under generalized conditions in order to solve equations in a Banach space setting. Some applications are suggested including Banach space valued functions of right fractional calculus, where all integrals are of Bochner-type. It follows [5].
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Convergence of Iterative Methods in Abstract Fractional Calculus
Functional Numerical Methods: Applications to Abstract Fractional Calculus, 2017Co-Authors: George A Anastassiou, Ioannis K ArgyrosAbstract:We present a semi-Local Convergence Analysis for a class of iterative methods under generalized conditions. Some applications are suggested including Banach space valued functions of fractional calculus, where all integrals are of Bochner-type.
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Iterative Methods in Abstract Fractional Calculus
Functional Numerical Methods: Applications to Abstract Fractional Calculus, 2017Co-Authors: George A Anastassiou, Ioannis K ArgyrosAbstract:The goal of this chapter is to present a semi-Local Convergence Analysis for some iterative methods under generalized conditions. The operator is only assumed to be continuous and its domain is open. Applications are suggested including Banach space valued functions of fractional calculus, where all integrals are of Bochner-type. It follows [5].