The Experts below are selected from a list of 360 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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extending the Convergence domain of the secant and moser method in banach space
Journal of Computational and Applied Mathematics, 2015Co-Authors: Ioannis K Argyros, Á. Alberto MagreñánAbstract:We present a new semilocal Convergence analysis for the Secant and the Moser method in order to approximate a solution of an equation in a Banach space setting. Using the method of recurrent relations and weaker sufficient Convergence Criteria than in earlier studies such as Amat et?al. (2014), Hernandez and Rubio (2007), Hernandez and Rubio (1999) and Hernandez and Rubio (2002) we increase the Convergence domain of these methods. The advantages are also obtained under less computational cost than in Amat et?al. (2014), Hernandez and Rubio (2007), Hernandez and Rubio (1999) and Hernandez and Rubio (2002). Numerical examples where the older Convergence Criteria are not satisfied but the new Convergence Criteria are satisfied are also provided in this study.
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extended Convergence results for the newton kantorovich iteration
Journal of Computational and Applied Mathematics, 2015Co-Authors: Ioannis K Argyros, Á. Alberto MagreñánAbstract:We present new semilocal and local Convergence results for the Newton-Kantorovich method. These new results extend the applicability of the Newton-Kantorovich method on approximate zeros by improving the Convergence domain and ratio given in earlier studies by Argyros (2003), Cianciaruso (2007), Smale (1986) and Wang (1999). These advantages are also obtained under the same computational cost. Numerical examples where the old sufficient Convergence Criteria are not satisfied but the new Convergence Criteria are satisfied are also presented in this study.
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EXPANDING THE Convergence DOMAIN FOR CHUN-STANICA-NETA FAMILY OF THIRD ORDER METHODS IN BANACH SPACES
Journal of the Korean Mathematical Society, 2015Co-Authors: Ioannis K Argyros, Santhosh George, Á. Alberto MagreñánAbstract:an Abstract. We present a semilocal Convergence analysis of a third order method for approximating a locally unique solution of an equation in a Banach space setting. Recently, this method was studied by Chun, Stanica and Neta. These authors extended earlier results by Kou, Li and others. Our Convergence analysis extends the applicability of these methods under less computational cost and weaker Convergence Criteria. Numerical examples are also presented to show that the earlier results cannot apply to solve these equations.
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Newton-Type Methods on Generalized Banach Spaces and Applications in Fractional Calculus
MDPI AG, 2015Co-Authors: George A. Anastassiou, Ioannis K ArgyrosAbstract:We present a semilocal Convergence study of Newton-type methods on a generalized Banach space setting to approximate a locally unique zero of an operator. Earlier studies require that the operator involved is Fréchet differentiable. In the present study we assume that the operator is only continuous. This way we extend the applicability of Newton-type methods to include fractional calculus and problems from other areas. Moreover, under the same or weaker conditions, we obtain weaker sufficient Convergence Criteria, tighter error bounds on the distances involved and an at least as precise information on the location of the solution. Special cases are provided where the old Convergence Criteria cannot apply but the new Criteria can apply to locate zeros of operators. Some applications include fractional calculus involving the Riemann-Liouville fractional integral and the Caputo fractional derivative. Fractional calculus is very important for its applications in many applied sciences
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A UNIFIED Convergence ANALYSIS FOR SECANT-TYPE METHODS
Journal of the Korean Mathematical Society, 2014Co-Authors: Ioannis K Argyros, Á. Alberto MagreñánAbstract:n´ Abstract. We present a unified local and semilocal Convergence analysis for secant-type 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 our semilocal Convergence Criteria can be weaker; the error bounds more precise and in the local case the Convergence balls can be larger and the error bounds tighter than in earlier studies such as (1-3,7-14,16,20,21) at least for the cases of Newton's method and the secant method. Numerical examples are also presented to illustrate the theoretical results obtained in this study.
Sanjay Khattri - One of the best experts on this subject based on the ideXlab platform.
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expanding the applicability of newton s method using smale s α theory
Journal of Computational and Applied Mathematics, 2014Co-Authors: Sanjay KhattriAbstract:We present a tighter Convergence analysis than earlier studies such as in Cianciaruso (2007), Guo (2007), Shen and Li (2010), Smale (1986, 1987), Wang and Zhao (1995), Wang (1999), Wang and Han (1990) of Newton's method using Smale's @a-theory by introducing the notion of the center @c"0-condition. In particular, in the semilocal Convergence case we show that if the center @c"0-condition is smaller than the @c-condition, then the new majorizing sequence is tighter than the old majorizing sequence. The new Convergence Criteria are weaker than the older Convergence Criteria. Furthermore, in the local Convergence case, we obtain a larger radius of Convergence and tighter error estimates on the distances involved. These improvements are obtained under the same computational cost. Numerical examples and applications are also provided in this study to show that the older results cannot apply but the new results apply to solve equations.
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a unifying semi local analysis for iterative algorithms of high Convergence order
Journal of Nonlinear Analysis and Optimization: Theory & Applications, 2013Co-Authors: Ioannis K Argyros, Sanjay KhattriAbstract:We present a unifying semi-local Convergence analysis of two-step Newton-type methods for solving nonlinear equations in a Banach space setting. Convergence order of these methods is higher than two. Our analysis expands the applicability of these methods by providing weaker Convergence Criteria and a Convergence analysis-which is tighter than earlier studies [see 1???4,24???34] ??? is also presented. Numerical examples illustrating the developed theoretical results are also given.
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An improved semilocal Convergence analysis for the Chebyshev method
Journal of Applied Mathematics and Computing, 2013Co-Authors: Ioannis K Argyros, Sanjay KhattriAbstract:We expand the applicability of the Chebyshev method for approximating a locally unique solution of nonlinear equations in a Banach space setting. Our majorizing sequences are finer than the known results in scientific literature and the Convergence Criteria can be weaker. Numerical examples are also presented which further validate the developed theoretical results.
Milivoj R Belic - One of the best experts on this subject based on the ideXlab platform.
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stationary optical solitons with sasa satsuma equation having nonlinear chromatic dispersion
Physics Letters A, 2020Co-Authors: Abdullahi Rashid Adem, Basetsana Pauline Ntsime, Anjan Biswas, Mir Asma, Mehmet Ekici, Seithuti P Moshokoa, Abdullah Kamis Alzahrani, Milivoj R BelicAbstract:Abstract This paper retrieves stationary optical solitons to Sasa–Satsuma equation that carries nonlinear chromatic dispersion. The solutions are in terms of Gauss' hypergeometric functions and consequently the Convergence Criteria are also listed.
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stationary optical solitons with nonlinear chromatic dispersion having quadratic cubic law of refractive index
Physics Letters A, 2020Co-Authors: Abdullahi Rashid Adem, Anjan Biswas, Mir Asma, Mehmet Ekici, Abdullah Kamis Alzahrani, Elsayed M E Zayed, Milivoj R BelicAbstract:Abstract Stationary optical solitons with quadratic–cubic law of nonlinear refractive index and nonlinear chromatic dispersion are retrieved. The model is considered with linear temporal evolution as well as with generalized temporal evolution. The results are in terms of Appell's hypergeometric function whose Convergence Criteria are also presented.
Magreñán, Á. Alberto - One of the best experts on this subject based on the ideXlab platform.
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Relaxed secant-type methods
Nonlinear Studies, 2018Co-Authors: Argyros, Ioannis K., Magreñán, Á. AlbertoAbstract:We present a unified local and semilocal Convergence analysis for secant-type 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, using both Lipschtiz and center Lipschitz conditions, our Convergence Criteria can be: weaker; the error bounds more precise and the Convergence balls larger than in earlier studies. Special cases such us Newton's method or Secant method are also presented. Numerical examples, including a Chandrasekhar equation and a boundary value problem, are also presented to illustrate the theoretical results obtained in this study
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Extending the Convergence domain of the Secant and Moser method in Banach Space
'Elsevier BV', 2017Co-Authors: Argyros, Ioannis K., Magreñán, Á. AlbertoAbstract:We present a new semilocal Convergence analysis for the Secant and the Moser method in order to approximate a solution of an equation in a Banach space setting. Using the method of recurrent relations and weaker sufficient Convergence Criteria than in earlier studies such as Amat et al. (2014), Hernandez and Rubio (2007), Hernandez and Rubio (1999) and Hernandez and Rubio (2002) we increase the Convergence domain of these methods. The advantages are also obtained under less computational cost than in Amat et al. (2014), Hernandez and Rubio (2007), Hernandez and Rubio (1999) and Hernandez and Rubio (2002). Numerical examples where the older Convergence Criteria are not satisfied but the new Convergence Criteria are satisfied are also provided in this study. (C) 2015 Elsevier B.V. All rights reserved
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Extended Convergence results for the Newton–Kantorovich iteration
'Elsevier BV', 2017Co-Authors: Argyros, Ioannis K., Magreñán, Á. AlbertoAbstract:We present new semilocal and local Convergence results for the Newton–Kantorovich method. These new results extend the applicability of the Newton–Kantorovich method on approximate zeros by improving the Convergence domain and ratio given in earlier studies by Argyros (2003), Cianciaruso (2007), Smale (1986) and Wang (1999). These advantages are also obtained under the same computational cost. Numerical examples where the old sufficient Convergence Criteria are not satisfied but the new Convergence Criteria are satisfied are also presented in this study
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Optimizing the applicability of a theorem by F. Potra for Newton-like methods
'Elsevier BV', 2017Co-Authors: Magreñán, Á. Alberto, Argyros, Ioannis K.Abstract:We present a new sufficient semilocal Convergence conditions for Newton-like methods in order to approximate a locally unique solution of an equation in a Banach space setting. This way, we expand the applicability of these methods in cases not covered in other studies such as Dennis (1971) [12], Ezquerro et al. (2000, 2010) [13,14], Kornstaedt (1975) [18], Potra and Ptak (1984) [24], Potra (1985, 1979, 1982, 1981, 1984) [23,25,26,27,28], Proinov (2010) [29], Schmidt (1978) [31] or Yamamoto (1987) [32]. The advantages of our approach also include a tighter Convergence analysis under the same computational cost. Applications, where the older Convergence Criteria are not satisfied but the new Convergence Criteria are satisfied are also given in this study. (C) 2014 Elsevier Inc. All rights reserved
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Extending the Convergence domain of Newton's method for twice Frechet differentiable operators
'World Scientific Pub Co Pte Lt', 2017Co-Authors: Argyros, Ioannis K., Magreñán, Á. AlbertoAbstract:We present a semi-local Convergence analysis of Newton's method in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Using center-Lipschitz condition on the first and the second Frechet derivatives, we provide under the same computational cost a new and more precise Convergence analysis than in earlier studies by Huang [A note of Kantorovich theorem for Newton iteration, J. Comput. Appl. Math. 47 (1993) 211-217] and Gutierrez [A new semilocal Convergence theorem for Newton's method, J. Comput. Appl. Math. 79 (1997) 131-145]. Numerical examples where the old Convergence Criteria cannot apply to solve nonlinear equations but the new Convergence Criteria are satisfied are also presented at the concluding section of this paper
Jinhua Wang - One of the best experts on this subject based on the ideXlab platform.
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Convergence Criteria of newton s method on lie groups
Fixed Point Theory and Applications, 2013Co-Authors: Jinhua Wang, Jenchih YaoAbstract:In the present paper, we study Newton’s method on Lie groups (independent of affine connections) for finding zeros of a mapping f from a Lie group to its Lie algebra. Under a generalized L-average Lipschitz condition of the differential of f, we establish a unified Convergence criterion of Newton’s method. As applications, we get the Convergence Criteria under the Kantorovich’s condition and the γ-condition, respectively. Moreover, applications to optimization problems are also provided.
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Convergence behavior of gauss newton s method and extensions of the smale point estimate theory
Journal of Complexity, 2010Co-Authors: Chong Li, Nuchun Hu, Jinhua WangAbstract:The notions of Lipschitz conditions with L average are introduced to the study of Convergence analysis of Gauss-Newton's method for singular systems of equations. Unified Convergence Criteria ensuring the Convergence of Gauss-Newton's method for one kind of singular systems of equations with constant rank derivatives are established and unified estimates of radii of Convergence balls are also obtained. Applications to some special cases such as the Kantorovich type conditions, @c-conditions and the Smale point estimate theory are provided and some important known results are extended and/or improved.