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Adaptive density estimation under weak dependence

Irène Gannaz, Olivier Wintenberger (2010)

ESAIM: Probability and Statistics

Assume that (Xt)t∈Z is a real valued time series admitting a common marginal density f with respect to Lebesgue's measure. [Donoho et al. Ann. Stat.24 (1996) 508–539] propose near-minimax estimators f ^ n based on thresholding wavelets to estimate f on a compact set in an independent and identically distributed setting. The aim of the present work is to extend these results to general weak dependent contexts. Weak dependence assumptions are expressed as decreasing bounds of covariance terms and are...

Adaptive finite element method for shape optimization

Pedro Morin, Ricardo H. Nochetto, Miguel S. Pauletti, Marco Verani (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution...

Adaptive finite element methods for elliptic problems: Abstract framework and applications

Serge Nicaise, Sarah Cochez-Dhondt (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We consider a general abstract framework of a continuous elliptic problem set on a Hilbert space V that is approximated by a family of (discrete) problems set on a finite-dimensional space of finite dimension not necessarily included into V. We give a series of realistic conditions on an error estimator that allows to conclude that the marking strategy of bulk type leads to the geometric convergence of the adaptive algorithm. These conditions are then verified for different concrete problems...

Adaptive finite element relaxation schemes for hyperbolic conservation laws

Christos Arvanitis, Theodoros Katsaounis, Charalambos Makridakis (2001)

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

We propose and study semidiscrete and fully discrete finite element schemes based on appropriate relaxation models for systems of Hyperbolic Conservation Laws. These schemes are using piecewise polynomials of arbitrary degree and their consistency error is of high order. The methods are combined with an adaptive strategy that yields fine mesh in shock regions and coarser mesh in the smooth parts of the solution. The computational performance of these methods is demonstrated by considering scalar...

Adaptive Finite Element Relaxation Schemes for Hyperbolic Conservation Laws

Christos Arvanitis, Theodoros Katsaounis, Charalambos Makridakis (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

We propose and study semidiscrete and fully discrete finite element schemes based on appropriate relaxation models for systems of Hyperbolic Conservation Laws. These schemes are using piecewise polynomials of arbitrary degree and their consistency error is of high order. The methods are combined with an adaptive strategy that yields fine mesh in shock regions and coarser mesh in the smooth parts of the solution. The computational performance of these methods is demonstrated by considering scalar...

Adaptive finite-time generalized outer synchronization between two different dimensional chaotic systems with noise perturbation

Zhi-cai Ma, Jie Wu, Yong-zheng Sun (2017)

Kybernetika

This paper is further concerned with the finite-time generalized outer synchronization between two different dimensional chaotic systems with noise perturbation via an adaptive controller. First of all, we introduce the definition of finite-time generalized outer synchronization between two different dimensional chaotic systems. Then, employing the finite-time stability theory, we design an adaptive feedback controller to realize the generalized outer synchronization between two different dimensional...

Adaptive hard-thresholding for linear inverse problems

Paul Rochet (2013)

ESAIM: Probability and Statistics

A number of regularization methods for discrete inverse problems consist in considering weighted versions of the usual least square solution. These filter methods are generally restricted to monotonic transformations, e.g. the Tikhonov regularization or the spectral cut-off. However, in several cases, non-monotonic sequences of filters may appear more appropriate. In this paper, we study a hard-thresholding regularization method that extends the spectral cut-off procedure to non-monotonic sequences....

Adaptive mesh refinement strategy for a non conservative transport problem

Benjamin Aymard, Frédérique Clément, Marie Postel (2014)

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

Long time simulations of transport equations raise computational challenges since they require both a large domain of calculation and sufficient accuracy. It is therefore advantageous, in terms of computational costs, to use a time varying adaptive mesh, with small cells in the region of interest and coarser cells where the solution is smooth. Biological models involving cell dynamics fall for instance within this framework and are often non conservative to account for cell division. In that case...

Adaptive modeling for free-surface flows

Simona Perotto (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

This work represents a first step towards the simulation of the motion of water in a complex hydrodynamic configuration, such as a channel network or a river delta, by means of a suitable “combination” of different mathematical models. In this framework a wide spectrum of space and time scales is involved due to the presence of physical phenomena of different nature. Ideally, moving from a hierarchy of hydrodynamic models, one should solve throughout the whole domain the most complex model (with...

Adaptive multiresolution methods

Margarete O. Domingues, Sônia M. Gomes, Olivier Roussel, Kai Schneider (2011)

ESAIM: Proceedings

These lecture notes present adaptive multiresolution schemes for evolutionary PDEs in Cartesian geometries. The discretization schemes are based either on finite volume or finite difference schemes. The concept of multiresolution analyses, including Harten’s approach for point and cell averages, is described in some detail. Then the sparse point representation method is discussed. Different strategies for adaptive time-stepping, like local scale dependent time stepping and time step control, are...

Adaptive Multiresolution Methods: Practical issues on Data Structures, Implementation and Parallelization*

K. Brix, S. Melian, S. Müller, M. Bachmann (2011)

ESAIM: Proceedings

The concept of fully adaptive multiresolution finite volume schemes has been developed and investigated during the past decade. Here grid adaptation is realized by performing a multiscale decomposition of the discrete data at hand. By means of hard thresholding the resulting multiscale data are compressed. From the remaining data a locally refined grid is constructed. The aim of the present work is to give a self-contained overview on the construction of an appropriate multiresolution analysis using...

Adaptive prediction of stock exchange indices by state space wavelet networks

Mietek A. Brdyś, Adam Borowa, Piotr Idźkowiak, Marcin T. Brdyś (2009)

International Journal of Applied Mathematics and Computer Science

The paper considers the forecasting of the Warsaw Stock Exchange price index WIG20 by applying a state space wavelet network model of the index price. The approach can be applied to the development of tools for predicting changes of other economic indicators, especially stock exchange indices. The paper presents a general state space wavelet network model and the underlying principles. The model is applied to produce one session ahead and five sessions ahead adaptive predictors of the WIG20 index...

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