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Interval methods for fixed-point problems [PDF]
Interval analysis is applied to the fixed-point problem x=ϕ(x) for continuous ϕ:S→S, where the space S is constructed from Cartesian products of the set R of real numbers, with componentwise definitions of arithmetic operations, ordering, and the product topology. With the aid of an interval inclusion φ:IS → IS in the interval space IS corresponding to
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A relaxed fixed point method for a mean curvature-based denoising model
Optim. Methods Softw., 2013Mean curvature-based energy minimization denoising model by Zhu and Chan offers one approach for restoring both smooth (no edges) and non-smooth (with edges) images.
Fenlin Yang, Ke Chen, Bo Yu, D. Fang
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IEEE transactions on industrial electronics (1982. Print), 2022
The sigmoid function is a widely used nonlinear activation function in neural networks. In this article, we present a modular approximation methodology for efficient fixed-point hardware implementation of the sigmoid function.
Zhe Pan+4 more
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The sigmoid function is a widely used nonlinear activation function in neural networks. In this article, we present a modular approximation methodology for efficient fixed-point hardware implementation of the sigmoid function.
Zhe Pan+4 more
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Extensions of the Fix-Point Method II: The Recursive Fix-Point Method
Économie appliquée, 1973Bodin Lennart. Extensions of the Fix-Point Method II: The Recursive Fix-Point Method. In: Économie appliquée, tome 26 n°2-4,1973. pp. 583-607.
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The sandwich method for computing fixed points
ACM SIGMAP Bulletin, 1973Many equilibrium and optimization problems in economics and operations research can be put in the form: Find x such that f(x) = x, where x is a nonnegative vector with component sum one and f is a continuous function (not necessarily differentiable, convex, or concave).
H. W. Kuhn, J. G. MacKinnon
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On the Fixed Point Method and Bloch’s Theorem
Michigan Mathematical Journal, 2021In this paper, via the contraction mapping principle, we give a proof of a Bloch-type theorem for normalized harmonic Bochner–Takahashi K-mappings and for solutions to equations of the form Pu=0, where P is a homogeneous differential operator with an analytic fundamental solution, that is, homogeneous elliptic operators with constant coefficients.
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Optimization, 2018
In this paper, we investigate the problem of finding a common solution to a fixed point problem involving demi-contractive operator and a variational inequality with monotone and Lipschitz continuous mapping in real Hilbert spaces.
A. Gibali, Y. Shehu
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In this paper, we investigate the problem of finding a common solution to a fixed point problem involving demi-contractive operator and a variational inequality with monotone and Lipschitz continuous mapping in real Hilbert spaces.
A. Gibali, Y. Shehu
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An improvement to the fixed point iterative method
Applied Mathematics and Computation, 2006The problem of convergence of the fixed point iterative method has been studied in this article. The main object of this article is to improve the convergence so that the number of iterations is reduced to just few iterations. A technique is presented to increase the order of convergence as much as desired.
Jafar Biazar, Alireza Amirteimoori
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Sandwich method for finding fixed points
Journal of Optimization Theory and Applications, 1975The sandwich method is a technique which uses simplicial subdivision to compute Brouwer fixed points and solve related problems, such as finding general economic equilibria. This paper presents a self-contained account of the sandwich method. It introduces the basic concepts of simplicial subdivision and the process ofsandwiching, demonstrates the ...
J. G. MacKinnon, H. W. Kuhn
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Extensions of the Fix-Point Method I: The GEID estimata and the fractional Fix-Point Method
Économie appliquée, 1973Ågren Anders. Extensions of the Fix-Point Method I: The GEID estimata and the fractional Fix-Point Method. In: Économie appliquée, tome 26 n°2-4,1973. pp. 561-582.
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