Asymptotic convergence

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Asymptotic convergence analysis of the proximal point algorithm

Asymptotic convergence analysis of the proximal point algorithm

The asymptotic convergence of the proximal point algorithm (PPA), for the solution of equations of type 0 e Tz, where T is a multivalued maximal monotone operator in a real [r]

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Asymptotic convergence rates of SWR methods for Schrödinger equations with an arbitrary number of subdomains

Asymptotic convergence rates of SWR methods for Schrödinger equations with an arbitrary number of subdomains

Keywords: Schr¨ odinger equation; Schwarz Waveform Relaxation; domain decomposition method; asymptotic convergence rate 1. Introduction We are interested in this paper in the analysis of the rate of convergence of some SWR methods by using an arbitrary number of subdomains. This study is an extension of existing results about the convergence of SWR algorithms on 2 subdomains [6, 7, 8]. We show that the convergence rates established for 2 subdomains are actually still accurate estimates for an arbitrary number of sufficiently large subdomains and bounded potentials. In this paper, we will mainly focus on the computation of contraction factors from Lipschitz continuous mappings involved in the proof of convergence of SWR methods. As a consequence, we will not introduce technical details about the full proof of convergence. Instead, we refer to several papers where the reader could find all the details of these proofs depending on the equation under consideration. For linear advection and diffusion reaction equations, we refer
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Non-asymptotic convergence bounds for Wasserstein approximation using point clouds

Non-asymptotic convergence bounds for Wasserstein approximation using point clouds

4 Numerical results In this section, we report some experimental results in dimension d = 2. Gray-scale image As we mentioned in the introduction, uniform optimal quantization allows to sparsely represent a (gray scale) image via points, clustered more closely in areas where the image is darker [4, 3]. On figure 3, we ploted the point clouds obtained after a single Lloyd step toward the density representing the image on the left (Puffin), starting from regular grids. The observed rate of convergence, N −1.00 , is coherent with the theoretical estimate log(N )/N of Remark 1.

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Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm

Non-asymptotic convergence analysis for the Unadjusted Langevin Algorithm

butions over a convex body. An adaptation of our result to non continuously differentiable potentials will appear in a forthcoming paper [ 14 ]. 3.3. Strongly log-concave densities More precise bounds can be obtained in the case where U is assumed to be strongly convex outside some ball; this assumption has been considered by [ 15 ] for convergence in the Wasserstein distance; see also [ 6 ].

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Convergence rate of an asymptotic preserving scheme for the diffusive limit of the p-system with damping

Convergence rate of an asymptotic preserving scheme for the diffusive limit of the p-system with damping

More precisely, they proved that the solution w of ( 1.1 ) converges to w = t (τ ,u) solution of ( 1.6 ) when time goes to infinity. In addition, they exhibited an estimation of the L ∞ -convergence rate in O(t −1/2 ). Next, by adopting energy estimate techniques, Nishihara and co-authors improved this convergence rate in [ 32 ] (see also the com- panion papers [ 30 , 31 ]). A generalization has been proposed by Bianchini et al in [ 3 ] to deal with general entropy dissipative hyperbolic systems of balance laws. Under the Shizuta-Kawashima condition, they established that the solutions under interest converge to a constant equilibrium state. In addition they exhibited the asymptotic convergence rate. Moreover, we refer the reader to the recent paper of Mei [ 26 ] where a wide litterature devoted to the long time asymptotic behaviour of the p−system with damping ( 1.1 ) is given.
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Strong convergence results for the asymptotic behavior of the 3D-shell model

Strong convergence results for the asymptotic behavior of the 3D-shell model

Abstract We revisit the asymptotic convergence properties – with respect to the thickness pa- rameter – of the earlier-proposed 3D-shell model. This shell model is very attractive for engineering applications, in particular due to the possibility of directly using a general 3D constitutive law in the corresponding finite element formulations. We establish strong con- vergence results for the 3D-shell model in the two main types of asymptotic regimes, namely, bending- and membrane-dominated behavior. This is an important achievement, as it com- pletely substantiates the asymptotic consistency of the 3D-shell model with 3D linearized isotropic elasticity.
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Cooperative Network Synchronization: Asymptotic Analysis

Cooperative Network Synchronization: Asymptotic Analysis

Abstract—Accurate clock synchronization is required for col- laborative operations among nodes across wireless networks. Compared with traditional layer-by-layer methods, cooperative network synchronization techniques lead to significant improve- ment in performance, efficiency, and robustness. This paper develops a framework for the performance analysis of cooperative network synchronization. We introduce the concepts of coopera- tive dilution intensity (CDI) and relative CDI to characterize the interaction between agents, which can be interpreted as proper- ties of a random walk over the network. Our approach enables us to derive closed-form asymptotic expressions of performance limits, relating them to the quality of observations as well as network topology.
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Convergence rates & asymptotic normality for series estimators

Convergence rates & asymptotic normality for series estimators

This paper has derived convergence rate and asymptotic normality results for series. estimators[r]

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La convergence internationale des structures de consommation

La convergence internationale des structures de consommation

iii) Ces distances sont évaluées à l'année t dont l'indice a été omis dans la notation, à cette date la distance globale Dn entre structures de consommation de tous les pays de l'écha[r]

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Détection de la convergence de processus de Markov

Détection de la convergence de processus de Markov

Conclusion et perspectives Dans cette th`ese, nous sommes partis d’un probl`eme de d´etection de la convergence de m´ethodes MCMC : comment d´eterminer empiriquement l’instant o`u l’algorithme a atteint son r´egime stationnaire. Pour cela nous nous sommes int´eress´es `a un ´echantillon d’algorithmes plutˆot qu’`a un seul. Ensuite nous avons fait le lien avec le ph´enom`ene de cutoff, qui se montre tr`es utile dans la d´etermination d’instants d’arrˆet d’algorithmes. Cependant, l’expression de l’instant de cutoff fait intervenir un param`etre inconnu qui mesure la vitesse de convergence de l’algorithme vers sa mesure stationnaire. Il est alors n´ecessaire de l’estimer. Dans cette prespective, nous avons introduit le temps d’atteinte d’un niveau par la moyenne arithm´etique d’une fonction de l’´echantillon. Nous avons alors ´etudi´e les propri´et´es asymptotiques de cette variable al´eatoire pour en d´eduire le comportement de l’estimateur. Au fur et `a mesure du cheminement de notre raisonnement, nous avons cependant laiss´e des questions en suspens, qui m´eritent d’ˆetre reprises. Au chapitre 3, plusieurs g´en´eralisations sont possibles, et elles font l’objet de l’article [7] avec J. Barrera et B. Ycart, qui est termin´e et qui sera soumis d’ici quelques semaines. Nous pouvons tout d’abord ´etudier le ph´enom`ene de cutoff pour des ´echantillons de processus non markoviens, pourvu qu’ils aient toujours la propri´et´e de convergence exponentielle vers leur loi stationnaire. Nous pouvons aussi supposer que les taux des convergences de chacun des processus margi- naux sont diff´erents. Enfin, il est aussi possible de montrer que le ph´enom`ene de cutoff survient ´egalement dans le cas o`u la vitesse de convergence du processus ´echantillonn´e est une fonction produit d’un polynˆome par une exponentielle d´ecroissante.
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Strong asymptotic independence on Wiener chaos

Strong asymptotic independence on Wiener chaos

References [1] S. Bai and M.S. Taqqu (2013): Multivariate limit theorems in the context of long-range dependence. J. Time Series Anal. 34, no. 6, 717-743. [2] S. Bourguin and J.-C. Breton (2013): Asymptotic Cramér type decomposition for Wiener and Wigner integrals. Infinite Dimensional Analysis, Quantum Probability and Related Topics 16, no. 1.

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Asymptotic Scattering by Poissonian Thermostats

Asymptotic Scattering by Poissonian Thermostats

Unlike the case of the Langevin thermostat [ 5 ], in the macroscopic limit the Poissonian thermostat scattering generates a continuous cloud of waves of frequencies different from that o[r]

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Asymptotic quasi-completeness and ZFC

Asymptotic quasi-completeness and ZFC

Another, quite simple example is the following: when we define the property of being a prime number within PA1, we do it on the natural numbers in such a way that we can say that on thes[r]

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Asymptotic Hecke algebras and involutions

Asymptotic Hecke algebras and involutions

0.1. In [11], a Hecke algebra module structure on a vector space spanned by the involutions in a Weyl group was defined and studied. In this paper this study is continued by relating it to the asymptotic Hecke algebra introduced in [6]. In particular we define a module over the asymptotic Hecke algebra which is spanned by the involutions in the Weyl group. We present a conjecture relating this module to equivariant vector bundles with respect to a group action on a finite set. This gives an explanation (not a proof) of a result of Kottwitz [3] in the case of classical Weyl groups, see 2.5. We also present a conjecture which realizes the module in [11] terms of an ideal in the Hecke algebra generated by a single element, see 3.4.
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Asymptotic lowest two-sided cell

Asymptotic lowest two-sided cell

In the remaining of this paper, we will prove the following theorem which is con- cerned with the asymptotic behaviour of the lowest two-sided cell, hence providing new evidences for the semicontinuity conjecture. Theorem 6.5. Let W be an irreducible affine Weyl group. There exists a finite set of rational hyperplanes H satisfying property (1) in Corollary 6.4 and satisfying the following property: if F is an H-facet which is contained in H ω i for some i,

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Asymptotic expansions of functional inverses

Asymptotic expansions of functional inverses

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignemen[r]

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Examples of automatic asymptotic expansions

Examples of automatic asymptotic expansions

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignemen[r]

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Asymptotic expansions for functionals processes

Asymptotic expansions for functionals processes

Unite´ de recherche INRIA Lorraine, Technopoˆle de Nancy-Brabois, Campus scientifique, 615 rue du Jardin Botanique, BP 101, 54600 VILLERS LE`S NANCY Unite´ de recherche INRIA Rennes, Iri[r]

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Asymptotic expansions and domain decomposition

Asymptotic expansions and domain decomposition

4. Geymonat, G., Hendili, S., Krasucki, F., Vidrascu, M.: The matched asymptotic expansion for the computation of the effective behavior of an elastic structure with a thin layer of holes. International Journal for Multiscale Computational Engineering 9(5), 529–542 (2011). DOI 10. 1615/IntJMultCompEng.v9.i5. URL http://hal.inria.fr/inria-00540992/en 5. Geymonat, G., Hendili, S., Krasucki, F., Vidrascu, M.: Matched asymptotic expansion method

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Pour une approche géographique de la convergence économique

Pour une approche géographique de la convergence économique

Arad et Timişoara. Ces dernières entretiennent des relations particulièrement étroites entre elles – via un trafic ferroviaire et routier dense – mais également avec la Hongrie. Cette zone étroite qui s'étend de la Yougoslavie à l'Ukraine est particulièrement attirée par l'Europe occidentale la remettant ainsi dans l'orbite de l'Europe centrale et germanique, dont elle fut un élément jusqu'en 1920 (Rey, 1996). Ce retour d'appartenance à la Mittleuropa a créé une situation de convergence économique locale. Cette zone s’est plus facilement ouverte au capitalisme occidental que d’autres régions roumaines (Cristescu, 2004). Les équipements commerciaux, les entreprises privées locales, étrangères et mixtes soulignent cette dynamique nouvelle. En outre, la présence d'une forte minorité hongroise et allemande dans cette zone facilite les relations que cette région de la Roumanie peut entretenir avec le reste de l'Europe. Le chômage y est moins fort que dans le reste de la Roumanie car d'autres activités sont venues se substituer très rapidement à la désindustrialisation engagée dans les années 1990. En outre, le secteur agricole y est plus performant qu'ailleurs en raison de la mise en place d'un système intensif combinant cultures céréalières et élevages bovins et en raison également d'une grande qualité du terroir du Banat. En revanche, la démographie est
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