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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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The Parametric Fix-Point (PFP) and the Algebraic Fix-Point (AFP) Methods
1981Publisher Summary The parametric fix-point (PFP) method can be applied to systems without identities and in the presence of identities. The structural coefficients of an identity are known in advance and therefore, the first semi-step in the step from s to s + 1 in the iterative procedure is omitted for the identities.
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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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Fixed point classification method for qualitative simulation
1997Qualitative simulation has become a successful method for predicting qualitatively distinct behaviors of physical systems. Yet it is quite weak in providing a global view on a system's behavior, e.g. its stability.
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