The Experts below are selected from a list of 378 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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Secant-like methods for solving nonlinear models with applications to chemistry
Journal of Mathematical Chemistry, 2018Co-Authors: Á. Alberto Magreñán, Ioannis K Argyros, Lara Orcos, Juan Antonio SiciliaAbstract:We present a local as well a Semilocal Convergence Analysis of secant-like methods under g eneral conditions in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The new conditions are more flexible than in earlier studies. This way we expand the applicability of these methods, since the new Convergence conditions are weaker. Moreover, these advantages are obtained under the same conditions as in earlier studies. Numerical examples are also provided in this study, where our results compare favorably to earlier ones.
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Improved Semilocal Convergence Analysis in Banach space with applications to chemistry
Journal of Mathematical Chemistry, 2018Co-Authors: Ioannis K Argyros, Á. Alberto Magreñán, Elena Giménez, Í. Sarría, Juan Antonio SiciliaAbstract:We present a new Semilocal Convergence Analysis for Secant methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our Analysis includes the computation of the bounds on the limit points of the majorizing sequences involved. Under the same computational cost on the parameters involved our Convergence criteria are weaker and the error bounds more precise than in earlier studies. A numerical example is also presented to illustrate the theoretical results obtained in this study.
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Robust Convergence of Newton's method for cone inclusion problem
A Contemporary Study of Iterative Methods, 2018Co-Authors: Á. Alberto Magreñán, Ioannis K ArgyrosAbstract:Abstract In this chapter, motivated by the idea of the restricted Convergence domains, we present a Convergence Analysis of Newton's method for cone inclusion problems. The Semilocal Convergence Analysis of Newton's method is also presented with different numerical examples in which we show the applicability of the theoretical results.
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On two high-order families of frozen Newton-type methods
Numerical Linear Algebra with Applications, 2017Co-Authors: Sergio Amat, Ioannis K Argyros, Sonia Busquier, Miguel Ángel Hernández-verónAbstract:Summary This paper is devoted to the study of two high-order families of frozen Newton-type methods. The methods are free of bilinear operators, which constitute the main limitation of the classical high-order iterative schemes. Both families are natural generalizations of an efficient third-order method. Although the methods are more demanding, a Semilocal Convergence Analysis is presented using weaker conditions.
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New improved Convergence Analysis for Newton-like methods with applications
Journal of Mathematical Chemistry, 2017Co-Authors: Á. Alberto Magreñán, Ioannis K Argyros, Juan Antonio SiciliaAbstract:We present a new Semilocal Convergence Analysis for Newton-like methods using restricted Convergence domains in a Banach space setting. The main goal of this study is to expand the applicability of these methods in cases not covered in earlier studies. The advantages of our approach include, under the same computational cost as previous studies, a more precise Convergence Analysis under the same computational cost on the Lipschitz constants involved. Numerical studies including a chemical application are also provided in this study.
Saïd Hilout - One of the best experts on this subject based on the ideXlab platform.
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Weaker Convergence conditions for the secant method
Applications of Mathematics, 2014Co-Authors: Ioannis K Argyros, Saïd HiloutAbstract:We use tighter majorizing sequences than in earlier studies to provide a Semilocal Convergence Analysis for the secant method. Our sufficient Convergence conditions are also weaker. Numerical examples are provided where earlier conditions do not hold but for which the new conditions are satisfied.
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expanding the applicability of inexact newton methods under smale s α γ theory
Applied Mathematics and Computation, 2013Co-Authors: Ioannis K Argyros, Sanjay Khattri, Saïd HiloutAbstract:We present a new Semilocal Convergence Analysis for an Inexact Newton Method (INM) using Smale's (@a,@c)-theory. Our approach is based on the concept of center-@c"0-condition. Developed sufficient Convergence conditions are weaker and the error estimates are tighter than those proposed in earlier studies such as Shen and Li [30,31], Guo [22], Smale [33-35], Morini [26], Argyros [2,8,9] and Argyros and Hilout [12]. Numerical examples illustrating the theoretical results are also provided in this study.
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Directional Secant-Type Methods for Solving Equations
Journal of Optimization Theory and Applications, 2013Co-Authors: Ioannis K Argyros, Saïd HiloutAbstract:A Semilocal Convergence Analysis for directional Secant-type methods in multidimensional space is provided. Using weaker hypotheses than the ones exploited by An and Bai, we provide a Semilocal Convergence Analysis with the following advantages: weaker Convergence conditions, larger Convergence domain, finer error estimates on the distances involved, and more precise information on the location of the solution. A numerical example, where our results apply to solve an equation but not the ones of An and Bai, is also provided. In a second example, we show how to implement the method.
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On a bilinear operator free third order method on Riemannian manifolds
Applied Mathematics and Computation, 2013Co-Authors: Sergio Amat, Saïd Hilout, Ioannis K Argyros, Sonia Busquier, R. Castro, S. PlazaAbstract:We present a Semilocal Convergence Analysis of a bilinear operator free third order method on Riemannian manifolds. Using a combination of generalized Lipschitz and center-Lipschitz conditions, we provide a Convergence Analysis which expands the applicability of the method even in the setting of nonlinear equations considered in earlier studies such as (cf. [4,9,38]).
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Majorizing sequences for iterative methods
Journal of Computational and Applied Mathematics, 2012Co-Authors: Ioannis K Argyros, Saïd HiloutAbstract:We provide Convergence results for very general majorizing sequences of iterative methods. Using our new concept of recurrent functions, we unify the Semilocal Convergence Analysis of Newton-type methods (NTM) under more general Lipschitz-type conditions. We present two very general majorizing sequences and we extend the applicability of (NTM) using the same information before Chen and Yamamoto (1989) [13], Deuflhard (2004) [16], Kantorovich and Akilov (1982) [19], Miel (1979) [20], Miel (1980) [21] and Rheinboldt (1968) [30]. Applications, special cases and examples are also provided in this study to justify the theoretical results of our new approach.
Á. Alberto Magreñán - One of the best experts on this subject based on the ideXlab platform.
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Improved Semilocal Convergence Analysis in Banach space with applications to chemistry
Journal of Mathematical Chemistry, 2018Co-Authors: Ioannis K Argyros, Á. Alberto Magreñán, Elena Giménez, Í. Sarría, Juan Antonio SiciliaAbstract:We present a new Semilocal Convergence Analysis for Secant methods in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Our Analysis includes the computation of the bounds on the limit points of the majorizing sequences involved. Under the same computational cost on the parameters involved our Convergence criteria are weaker and the error bounds more precise than in earlier studies. A numerical example is also presented to illustrate the theoretical results obtained in this study.
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Secant-like methods for solving nonlinear models with applications to chemistry
Journal of Mathematical Chemistry, 2018Co-Authors: Á. Alberto Magreñán, Ioannis K Argyros, Lara Orcos, Juan Antonio SiciliaAbstract:We present a local as well a Semilocal Convergence Analysis of secant-like methods under g eneral conditions in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. The new conditions are more flexible than in earlier studies. This way we expand the applicability of these methods, since the new Convergence conditions are weaker. Moreover, these advantages are obtained under the same conditions as in earlier studies. Numerical examples are also provided in this study, where our results compare favorably to earlier ones.
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Robust Convergence of Newton's method for cone inclusion problem
A Contemporary Study of Iterative Methods, 2018Co-Authors: Á. Alberto Magreñán, Ioannis K ArgyrosAbstract:Abstract In this chapter, motivated by the idea of the restricted Convergence domains, we present a Convergence Analysis of Newton's method for cone inclusion problems. The Semilocal Convergence Analysis of Newton's method is also presented with different numerical examples in which we show the applicability of the theoretical results.
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New improved Convergence Analysis for Newton-like methods with applications
Journal of Mathematical Chemistry, 2017Co-Authors: Á. Alberto Magreñán, Ioannis K Argyros, Juan Antonio SiciliaAbstract:We present a new Semilocal Convergence Analysis for Newton-like methods using restricted Convergence domains in a Banach space setting. The main goal of this study is to expand the applicability of these methods in cases not covered in earlier studies. The advantages of our approach include, under the same computational cost as previous studies, a more precise Convergence Analysis under the same computational cost on the Lipschitz constants involved. Numerical studies including a chemical application are also provided in this study.
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Extending the applicability of the local and Semilocal Convergence of Newton's method
Applied Mathematics and Computation, 2017Co-Authors: Ioannis K Argyros, Á. Alberto MagreñánAbstract:We present a local as well a Semilocal Convergence Analysis for Newton's method in a Banach space setting. Using the same Lipschitz constants as in earlier studies, we extend the applicability of Newton's method as follows: local case: a larger radius is given as well as more precise error estimates on the distances involved. Semilocal case: the Convergence domain is extended; the error estimates are tighter and the information on the location of the solution is at least as precise as before. Numerical examples further justify the theoretical results.
Sanjay Khattri - One of the best experts on this subject based on the ideXlab platform.
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Local Convergence of an at least sixth-order method in Banach spaces
Journal of Fixed Point Theory and Applications, 2019Co-Authors: I. K. Argyros, Sanjay Khattri, S. GeorgeAbstract:We present a local Convergence Analysis of an at least sixth-order family of methods to approximate a locally unique solution of nonlinear equations in a Banach space setting. The Semilocal Convergence Analysis of this method was studied by Amat et al. in (Appl Math Comput 206:164–174, 2008 ; Appl Numer Math 62:833–841, 2012 ). This work provides computable Convergence ball and computable error bounds. Numerical examples are also provided in this study.
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An improved Semilocal Convergence Analysis for the midpoint method
2016Co-Authors: Ioannis K Argyros, Sanjay KhattriAbstract:We expand the applicability of the midpoint method for approximating a locally unique solutionof nonlinear equations in a Banach space setting. Our majorizing sequences are finer than theknown results in scientific literature [1,3,4,5,6,7,8,9,10,11,19,20,21,23] and the Convergencecriteria can be weaker. Finally, numerical work is reported that compares favorably to the existingapproaches in the literature [6, 8--16, 24--26,28].
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On the Convergence of Broyden’s method in Hilbert spaces
Applied Mathematics and Computation, 2014Co-Authors: Ioannis K Argyros, Yeol Je Cho, Sanjay KhattriAbstract:Abstract In this paper, we present a new Semilocal Convergence Analysis for an inverse free Broyden’s method in a Hilbert space setting. In the Analysis, we apply our new idea of recurrent functions concepts of divided differences of order one and Lipschitz/center–Lipschitz conditions on the operator involved. Our Analysis extends the applicability of Broyden’s method in cases not covered before. Finally, we give an example to illustrate the main result in this paper.
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expanding the applicability of inexact newton methods under smale s α γ theory
Applied Mathematics and Computation, 2013Co-Authors: Ioannis K Argyros, Sanjay Khattri, Saïd HiloutAbstract:We present a new Semilocal Convergence Analysis for an Inexact Newton Method (INM) using Smale's (@a,@c)-theory. Our approach is based on the concept of center-@c"0-condition. Developed sufficient Convergence conditions are weaker and the error estimates are tighter than those proposed in earlier studies such as Shen and Li [30,31], Guo [22], Smale [33-35], Morini [26], Argyros [2,8,9] and Argyros and Hilout [12]. Numerical examples illustrating the theoretical results are also provided in this study.
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On an iterative algorithm of Ulm-type for solving equations
2013Co-Authors: Ioannis K Argyros, Sanjay KhattriAbstract:We provide a Semilocal Convergence Analysis of an iterative algorithm for solving nonlinear operator equations in a Banach space setting. This algorithm is of order \(1.839\ldots\), and has already been studied in [3, 8, 18, 20]. Using our new idea of recurrent functions we show that a finer Analysis is possible with sufficient Convergence conditions that can be weaker than before, and under the same computational cost. Numerical examples are also provided in this study.
Himanshu Kumar - One of the best experts on this subject based on the ideXlab platform.
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On Semilocal Convergence of three-step Kurchatov method under weak condition
Arabian Journal of Mathematics, 2021Co-Authors: Himanshu KumarAbstract:The purpose of this paper to establish the Semilocal Convergence Analysis of three-step Kurchatov method under weaker conditions in Banach spaces. We construct the recurrence relations under the assumption that involved first-order divided difference operators satisfy the $$\omega $$ ω condition. Theorems are given for the existence-uniqueness balls enclosing the unique solution. The application of the iterative method is shown by solving nonlinear system of equations and nonlinear Hammerstein-type integral equations. It illustrates the theoretical development of this study.
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Three Step Kurchatov Method for Nondifferentiable Operators
International Journal of Applied and Computational Mathematics, 2017Co-Authors: Himanshu Kumar, P. K. ParidaAbstract:In this paper we find the order of Convergence and Semilocal Convergence of three step Kurchatov-type method. We also analyze the efficiency index and computational efficiency of this method. The Semilocal Convergence Analysis of method has been established by using recurrence relations under the assumption of first order divided difference operators satisfy Lipschitz condition. The Convergence theorem and domain of parameters of the method has also been included. The applicability of the proposed Convergence Analysis is illustrated by solving some numerical examples.
