The Experts below are selected from a list of 242784 Experts worldwide ranked by ideXlab platform
Saïd Hilout - One of the best experts on this subject based on the ideXlab platform.
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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: 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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A Convergence Analysis for directional two-step Newton methods
Numerical Algorithms, 2010Co-Authors: Saïd HiloutAbstract:A semilocal Convergence Analysis for directional two-step Newton methods in a Hilbert space setting is provided in this study. Two different techniques are used to generate the sufficient Convergence results, as well as the corresponding error bounds. The first technique uses our new idea of recurrent functions, whereas the second uses recurrent sequences. We also compare the results of the two techniques.
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an improved local Convergence Analysis for newton steffensen type method
Journal of Applied Mathematics and Computing, 2010Co-Authors: 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).
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an improved local Convergence Analysis for secant like method
East Asian mathematical journal, 2007Co-Authors: Saïd HiloutAbstract:Abstract. We provide a local Convergence Analysis for Secant–like algorithm for solving nonsmooth variational inclusions in Ba-nach spaces. An existence–Convergence theorem and an improve-ment of the ratio of Convergence of this algorithm are given undercenter–conditioned divided difference and Aubin’s continuity con-cept. Our result compare favorably with related obtained in [16]. 1. IntroductionThis paper considers the problem of approximating a locally uniquesolution of nondifferentiable generalized equations using an unipara-metric secant–type algorithm. Let X , Y be two Banach spaces, F isa continuous function from X into Y and G is a set–valued map from X to the subsets of Y with closed graph. We consider a generalizedequation in the form(1.1) 0 ∈ F ( x )+ G ( x ) . Generalized equations (1.1) was introduced by Robinson [20], [21].(1.1) is an abstract model including mathematical programming prob-lems, variational inequalities, optimal control, complementarity prob-lems and other fields.For approximating locally the unique solution
Kyle S. Talbot - One of the best experts on this subject based on the ideXlab platform.
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Unified Convergence Analysis of Numerical Schemes for a Miscible Displacement Problem
Foundations of Computational Mathematics, 2019Co-Authors: Jérôme Droniou, Robert Eymard, Alain Prignet, Kyle S. TalbotAbstract:This article performs a unified Convergence Analysis of a variety of numerical methods for a model of the miscible displacement of one incompressible fluid by another through a porous medium. The unified Analysis is enabled through the framework of the gradient discretisation method for diffusion operators on generic grids. We use it to establish a novel Convergence result in $$L^\infty (0,T; L^2(\Omega ))$$ L ∞ ( 0 , T ; L 2 ( Ω ) ) of the approximate concentration using minimal regularity assumptions on the solution to the continuous problem. The convection term in the concentration equation is discretised using a centred scheme. We present a variety of numerical tests from the literature, as well as a novel analytical test case. The performance of two schemes is compared on these tests; both are poor in the case of variable viscosity, small diffusion and medium to small time steps. We show that upstreaming is not a good option to recover stable and accurate solutions, and we propose a correction to recover stable and accurate schemes for all time steps and all ranges of diffusion.
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unified Convergence Analysis of numerical schemes for a miscible displacement problem
arXiv: Numerical Analysis, 2017Co-Authors: Jérôme Droniou, Robert Eymard, Alain Prignet, Kyle S. TalbotAbstract:This article performs a unified Convergence Analysis of a variety of numerical methods for a model of the miscible displacement of one incompressible fluid by another through a porous medium. The unified Analysis is enabled through the framework of the gradient discretisation method for diffusion operators on generic grids. We use it to establish a novel Convergence result in $L^\infty(0,T; L^2(\Omega))$ of the approximate concentration using minimal regularity assumptions on the solution to the continuous problem. The convection term in the concentration equation is discretised using a centred scheme, whose performance we compare to the upwind scheme by means of numerical experiments.
Yu Zhu - One of the best experts on this subject based on the ideXlab platform.
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mean square Convergence Analysis of adaline training with minimum error entropy criterion
IEEE Transactions on Neural Networks, 2010Co-Authors: Yu ZhuAbstract:Recently, the minimum error entropy (MEE) criterion has been used as an information theoretic alternative to traditional mean-square error criterion in supervised learning systems. MEE yields nonquadratic, nonconvex performance surface even for adaptive linear neuron (ADALINE) training, which complicates the theoretical Analysis of the method. In this paper, we develop a unified approach for mean-square Convergence Analysis for ADALINE training under MEE criterion. The weight update equation is formulated in the form of block-data. Based on a block version of energy conservation relation, and under several assumptions, we carry out the mean-square Convergence Analysis of this class of adaptation algorithm, including mean-square stability, mean-square evolution (transient behavior) and the mean-square steady-state performance. Simulation experimental results agree with the theoretical predictions very well.
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mean square Convergence Analysis of adaline training with minimum error
2010Co-Authors: Entropy Criterion, Yu ZhuAbstract:Recently, the minimum error entropy (MEE) cri- terion has been used as an information theoretic alternative to traditional mean-square error criterion in supervised learning systems. MEE yields nonquadratic, nonconvex performance sur- face even for adaptive linear neuron (ADALINE) training, which complicates the theoretical Analysis of the method. In this paper, we develop a unified approach for mean-square Convergence Analysis for ADALINE training under MEE criterion. The weight update equation is formulated in the form of block-data. Based on a block version of energy conservation relation, and under several assumptions, we carry out the mean-square Convergence Analysis of this class of adaptation algorithm, including mean-square stability, mean-square evolution (transient behavior) and the mean-square steady-state performance. Simulation experimental results agree with the theoretical predictions very well.
Mengyin Fu - One of the best experts on this subject based on the ideXlab platform.
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A novel delta operator Kalman filter design and Convergence Analysis
IEEE Transactions on Circuits and Systems I: Regular Papers, 2011Co-Authors: Hongjiu Yang, Peng Shi, Yuanqing Xia, Mengyin FuAbstract:This paper focuses on the development of a delta operator Kalman filter and its Convergence Analysis. The delta operator Kalman filter is designed to estimate the state vectors of a delta operator system. Note that the designed delta operator Kalman filter can express both continuous-time and discrete-time cases. Then, the Convergence Analysis of the delta operator Kalman filter is also investigated by using Lyapunov approach in delta domain. Furthermore, this paper gives fundamental results for the Analysis and application of the delta operator Kalman filter as a state observer in an inverted pendulum model. Some experimental results of an inverted pendulum on a laboratory-scale setup are presented to illustrate the effectiveness of the designed Kalman filter and its implementation.
Xiaoming Yuan - One of the best experts on this subject based on the ideXlab platform.
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Convergence Analysis of primal dual algorithms for a saddle point problem from contraction perspective
Siam Journal on Imaging Sciences, 2012Co-Authors: Xiaoming YuanAbstract:Recently, some primal-dual algorithms have been proposed for solving a saddle-point problem, with particular applications in the area of total variation image restoration. This paper focuses on the Convergence Analysis of these primal-dual algorithms and shows that their involved parameters (including step sizes) can be significantly enlarged if some simple correction steps are supplemented. Some new primal-dual-based methods are thus proposed for solving the saddle-point problem. We show that these new methods are of the contraction type: the iterative sequences generated by these new methods are contractive with respect to the solution set of the saddle-point problem. The global Convergence of these new methods thus can be obtained within the analytic framework of contraction-type methods. The novel study on these primal-dual algorithms from the perspective of contraction methods substantially simplifies existing Convergence Analysis. Finally, we show the efficiency of the new methods numerically.
