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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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1998
In this somewhat technical section we look at the theory of fibrewise ENRs and ANRs. The results are mostly due to Dold [47]. Our restriction to base spaces which are ENRs allows us to simplify the exposition at several points. We begin with a discussion of some of the properties of ENRs and ANRs which we have already used in earlier sections.
Michael Charles Crabb +1 more
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In this somewhat technical section we look at the theory of fibrewise ENRs and ANRs. The results are mostly due to Dold [47]. Our restriction to base spaces which are ENRs allows us to simplify the exposition at several points. We begin with a discussion of some of the properties of ENRs and ANRs which we have already used in earlier sections.
Michael Charles Crabb +1 more
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A boundary perturbation interior point homotopy method for solving fixed point problems
In this paper, a boundary perturbation interior point homotopy method is proposed to give a constructive proof of the general Brouwer fixed point theorem and thus solve fixed point problems in a class of nonconvex sets. Compared with the previous results,
Menglong Su, Shaoyun Shi
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Fixed-Point Quasi-Newton Methods
SIAM Journal on Numerical Analysis, 1992This paper studies iterative methods of the form (1) \(x_{k+1}=\Phi(x_ k,E_ k)\) where \(x_ k\in\mathbb{R}^ n\), and \(E_ k\) belongs to some parameter space. Three examples of methods which may be written in this form are given, namely quasi-Newton methods for nonlinear systems, sequential quadratic programming and nonlinear complementarity.
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A fixed point multiple shooting method
Computing, 1988A method is proposed for solving ordinary two-point boundary value problems of a certain type. It works if the problem can be transformed into a contracting fixed point equation by means of a Green's function which need not be known for the process. It is similar to multiple shooting but much simpler.
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The fixed point method in analysis.
1936zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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Fixed-Point Methods in Parametric Model Checking
2015We present a general framework for the synthesis of the constraints under which the selected properties hold in a class of models with discrete transitions, together with Boolean encoding - based method of implementing the theory. We introduce notions of parametric image and preimage, and show how to use them to build fixed-point algorithms for ...
Michal Knapik, Wojciech Penczek
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On Spurious Fixed Points of Runge–Kutta Methods
Journal of Computational Physics, 1997This paper deals with the existence and generation of spurious fixed points in the numerical integration of autonomous scalar differential equations \(u'=f(u)\) by means of Runge-Kutta methods. Since the numerical method can be written in the form \(u_{n+1}= u_n+ h\phi(u_n,h)\), where \(\phi\) is the increment function, it can be considered as a ...
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