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Convergence analysis for principal component flows

Shintaro Yoshizawa, Uwe Helmke, Konstantin Starkov (2001)

International Journal of Applied Mathematics and Computer Science

A common framework for analyzing the global convergence of several flows for principal component analysis is developed. It is shown that flows proposed by Brockett, Oja, Xu and others are all gradient flows and the global convergence of these flows to single equilibrium points is established. The signature of the Hessian at each critical point is determined.

Convergence behavior of the (1 +, λ) evolution strategy on the ridge functions.

Ahmet Irfan Oyman, Hans-Georg Beyer, Hans-Paul Schwefel (2000)

Mathware and Soft Computing

The convergence behavior of (1 +, λ)-ES is investigated at parabolic ridge, sharp ridge, and at the general case of the ridge functions. The progress rate, the distance to the ridge axis, the success rate, and the success probability are used in the analysis. The strong dependency of the (1 + λ)-ES to the initial conditions is shown using parabolic ridge test function when low distances to the ridge axis are chosen as the start value. The progress rate curve and the success probability curve of...

Convergence of the time-discretized monotonic schemes

Julien Salomon (2007)

ESAIM: Mathematical Modelling and Numerical Analysis

Many numerical simulations in (bilinear) quantum control use the monotonically convergent Krotov algorithms (introduced by Tannor et al. [Time Dependent Quantum Molecular Dynamics (1992) 347–360]), Zhu and Rabitz [J. Chem. Phys. (1998) 385–391] or their unified form described in Maday and Turinici [J. Chem. Phys. (2003) 8191–8196]. In Maday et al. [Num. Math. (2006) 323–338], a time discretization which preserves the property of monotonicity has been presented. This paper introduces a proof of...

Conversion of regular expressions into realtime automata

Viliam Geffert, L'ubomíra Ištoňová (2006)

RAIRO - Theoretical Informatics and Applications

We consider conversions of regular expressions into k-realtime finite state automata, i.e., automata in which the number of consecutive uses of ε-transitions, along any computation path, is bounded by a fixed constant k. For 2-realtime automata, i.e., for automata that cannot change the state, without reading an input symbol, more than two times in a row, we show that the conversion of a regular expression into such an automaton produces only O(n) states, O(nlogn) ε-transitions, and O(n) alphabet-transitions....

Convolutive decomposition and fast summation methods for discrete-velocity approximations of the Boltzmann equation

Clément Mouhot, Lorenzo Pareschi, Thomas Rey (2013)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Discrete-velocity approximations represent a popular way for computing the Boltzmann collision operator. The direct numerical evaluation of such methods involve a prohibitive cost, typically O(N2d + 1) where d is the dimension of the velocity space. In this paper, following the ideas introduced in [C. Mouhot and L. Pareschi, C. R. Acad. Sci. Paris Sér. I Math. 339 (2004) 71–76, C. Mouhot and L. Pareschi, Math. Comput. 75 (2006) 1833–1852], we derive fast summation techniques for the evaluation of...

Conway's Games and Some of their Basic Properties

Robin Nittka (2011)

Formalized Mathematics

We formulate a few basic concepts of J. H. Conway's theory of games based on his book [6]. This is a first step towards formalizing Conway's theory of numbers into Mizar, which is an approach to proving the existence of a FIELD (i.e., a proper class that satisfies the axioms of a real-closed field) that includes the reals and ordinals, thus providing a uniform, independent and simple approach to these two constructions that does not go via the rational numbers and hence does for example not need...

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