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Interval methods for fixed-point problems [PDF]

open access: possibleNumerical Functional Analysis and Optimization, 1987
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., 2013
Mean 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
semanticscholar   +1 more source

A Modular Approximation Methodology for Efficient Fixed-Point Hardware Implementation of the Sigmoid Function

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
semanticscholar   +1 more source

Extensions of the Fix-Point Method II: The Recursive Fix-Point Method

Économie appliquée, 1973
Bodin 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, 1973
Many 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, 2021
In 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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An efficient iterative method for finding common fixed point and variational inequalities in Hilbert spaces

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
semanticscholar   +1 more source

An improvement to the fixed point iterative method

Applied Mathematics and Computation, 2006
The 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, 1975
The 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, 1973
Ågren 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.
openaire   +2 more sources

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