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Analysis of the Convergence and Generalization of AA1
Journal of Parallel and Distributed Computing, 1995AA1 is an incremental learning algorithm for Adaptive Self-Organizing Concurrent Systems (ASOCS). ASOCS are self-organizing, dynamically growing networks of computing nodes. AA1 learns by discrimination and implements knowledge in a distributed fashion over all the nodes. This paper reviews AA1 from the perspective of convergence and generalization.
Giraud-Carrier, Christophe +1 more
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A convergence analysis of the ADM and an application
Applied Mathematics and Computation, 2005The Adomian decomposition method (ADM) is applied to the modified Korteweg-de Vries equation. This method yields exact and approximate solutions of nonlinear problems without transforming the equation. The solution is expressed in a series and the basis functions are obtained via recursions.
Dogan Kaya, Ibrahim E. Inan
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Convergence Structures in Numerical Analysis
Zeitschrift für Analysis und ihre Anwendungen, 1996The paper deals — under the viewpoint of topology — with discrete Cauchy spaces, which are spaces where a discrete Cauchy structure (t,\mathcal C) (with t being a ...
Gähler, Siegfried +1 more
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2004
Proving convergence of the various optimization algorithms is a delicate exercise. In general, it is helpful to consider local and global convergence patterns separately. The local convergence rate of an algorithm provides a useful benchmark for comparing it to other algorithms. On this basis, Newton’s method wins hands down. However, the tradeoffs are
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Proving convergence of the various optimization algorithms is a delicate exercise. In general, it is helpful to consider local and global convergence patterns separately. The local convergence rate of an algorithm provides a useful benchmark for comparing it to other algorithms. On this basis, Newton’s method wins hands down. However, the tradeoffs are
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Convergent Systems: Analysis and Synthesis
2005In this paper we extend the notion of convergent systems defined by B.P. Demidovich and introduce the notions of uniformly, exponentially convergent and input-to-state convergent systems. Basic (interconnection) properties of such systems are established. Sufficient conditions for input-to-state convergence are presented.
Pavlov, A. +2 more
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Convergence analysis of active contours
Image and Vision Computing, 2008Active contours are very useful tools in image segmentation and object tracking in video sequences. The practical implementations are built with an iterative algorithm based on a second order system defined in the spatial domain, where the elasticity and rigidity are the static parameters for its characterization and mass and damping are the dynamic ...
Rafael Verdú Monedero +2 more
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On the convergence of validity interval analysis
IEEE Transactions on Neural Networks, 2000Validity interval analysis (VIA) is a generic tool for analyzing the input-output behavior of feedforward neural networks. VIA is a rule extraction technique that relies on a rule refinement algorithm. The rules are of the form R(i)-->R(0) which reads if the input of the neural network is in the region R(i), then its output is in the region R(0), where
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Convergence analysis of the CMA blind equalizer
IEEE Transactions on Communications, 1995The convergence behaviour of the constant modulus algorithm (CMA) is analytically evaluated in terms of the mean and the variance of the equalized sequence conditioned on the transmitted symbol, thus characterizing the dispersion pattern of the equalized samples around the QAM constellation points.
CUSANI, Roberto, A. Laurenti
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Convergence Analysis of Affinity Propagation
2009Recently, Frey & Dueck proposed a novel clustering algorithm named affinity propagation (AP), which has been shown to be powerful as it costs much less time and reaches much lower error. However, its convergence property has not been studied in theory. In this paper, we focus on convergence property of the algorithm.
Jian Yu 0001, Caiyan Jia
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Convergence Analysis for Three Parareal Solvers
SIAM Journal on Scientific Computing, 2015Summary: We analyze in this paper the convergence properties of the parareal algorithm for the symmetric positive definite problem \(\mathbf{u}'+A\mathbf{u}=g\). The coarse propagator \(\mathcal{G}\) is fixed to the backward-Euler method and three time integrators are chosen for the \(\mathcal{F}\)-propagator: the trapezoidal rule, the third-order ...
Shu-Lin Wu, Tao Zhou
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