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Numerical Methods for First and Second Order Fully Nonlinear Partial Differential Equations

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A multi-iterate method to solve systems of nonlinear equations

Michel Bierlaire, Michaël Clément Louis Ghislain Thémans, Frank Crittin

We propose an extension of secant methods for nonlinear equations using a population of previous iterates. Contrarily to classical secant methods, where exact interpolation is used, we prefer a least squares approach to calibrate the linear model. We propo ...

2007

Prédiction spatiale en présence d'erreurs substitutives et modélisation par drap stable

Baptiste Fournier

In geostatistics, the presence of outlying data is more the rule than the exception. Moreover, the statistical analysis of data contaminated by outliers requires caution, particularly when a spatial dependence exists. In order to take into account these po ...

EPFL2007

Configurational entropy of hard spheres

Giuseppe Foffi

We numerically calculate the configurational entropy Sconf of a binary mixture of hard spheres, by using a perturbed Hamiltonian method trapping the system inside a given state, which requires fewer assumptions than the previous methods (Speedy 1998 Mol.Ph ...

2007

Accelerating Distributed Consensus Using Extrapolation

Pascal Frossard, Effrosyni Kokiopoulou

In the past few years, the problem of distributed consensus has received a lot of attention, particularly in the framework of ad hoc sensor networks. Most methods proposed in the literature attack this problem by distributed linear iterative algorithms, wi ...

2007

Deflation in Krylov subspace methods and distance to uncontrollability

Daniel Kressner

The task of extracting from a Krylov decomposition the approximation to an eigenpair that yields the smallest backward error can be phrased as finding the smallest perturbation which makes an associated matrix pair uncontrollable. Exploiting this relations ...

2007

Analysis and numerical simulation of viscoelastic flows

Andrea Bonito

Mathematical and numerical aspects of viscoelastic flows are investigated here. Two simplified mathematical models are considered. They are motivated by a splitting algorithm for solving viscoelastic flows with free surfaces. The first model is a simplifie ...

EPFL2006

Numerical methods for multiscale problems

Assyr Abdulle

The subject of this workshop was numerical methods that preserve geometric properties of the flow of an ordinary or partial differential equation: symplectic and multisymplectic integrators for Hamiltonian systems, symmetric integrators for reversible syst ...

EMS2006

Scientific Computing with MATLAB and Octave

Alfio Quarteroni

This textbook is an introduction to Scientific Computing, in which several numerical methods for the computer solution of certain classes of mathematical problems are illustrated. The authors show how to compute the zeros or the integrals of continuous fun ...

Springer2006

Finite element methods with patches and applications

Joël Wagner

Theoretical and numerical aspects of multi-scale problems are investigated. On one hand, mathematical analysis is done on a new method for numerically solving problems with multi-scale behavior using multiple levels of not necessarily nested grids. A parti ...

EPFL2006

A multi-iterate method to solve systems of nonlinear equations

Michel Bierlaire, Michaël Clément Louis Ghislain Thémans, Frank Crittin

2006