Concept

Polynôme d'Hermite

Publications associées (136)

Computation of connection coefficients and measure modifications for orthogonal polynomials

We observe that polynomial measure modifications for families of univariate orthogonal polynomials imply sparse connection coefficient relations. We therefore propose connecting L (2) expansion coefficients between a polynomial family and a modified family ...

Springer Verlag2012

Application of Legendrian Foliations in Differential Flatness Problems

Philippe Müllhaupt, Basile Graf

Instances of control systems are presented for which dynamical feedback linearizability can be assessed from differential forms of highest relative degree after some “contact” transformation has been applied. This bypasses the need to find a polynomial dif ...

2012

MATHICSE Technical Report : Sparse spectral approximations for computing polynomial functionals

Fabio Nobile

We give a new fast method for evaluating sprectral approximations of nonlinear polynomial functionals. We prove that the new algorithm is convergent if the functions considered are smooth enough, under a general assumption on the spectral eigenfunctions th ...

MATHICSE2012

Sparse spectral approximations for computing polynomial functionals

Fabio Nobile

2012

Exponential splines and minimal-support bases for curve representation

Michaël Unser, Philippe Thévenaz, Ricard Delgado Gonzalo

Our interest is to characterize the spline-like integer-shift-invariant bases capable of reproducing exponential polynomial curves. We prove that any compact-support function that reproduces a subspace of the exponential polynomials can be expressed as the ...

Elsevier2012

A coordinate system for Gaussian Networks

Emmanuel Abbé

This paper studies network information theory problems where the external noise is Gaussian distributed. In particular, the Gaussian broadcast channel with coherent fading and the Gaussian interference channel are investigated. It is shown that in these pr ...

Institute of Electrical and Electronics Engineers2012

Estimation of multiple phases from a single fringe pattern in digital holographic interferometry

Pramod Rastogi, Sai Siva Gorthi

Simultaneous measurement of multidimensional displacements using digital holographic interferometry involves multi-directional illumination of the deformed object and requires the reliable estimation of the resulting multiple interference phase distributio ...

Optical Society of America2012

Three dimensional shape measurement using high-order instantaneous moments based fringe projection method

Pramod Rastogi, Sai Siva Gorthi

Fringe projection techniques are popular tools for three-dimensional shape measurement in optical metrology. In these techniques, the information about the shape or the surface profile of an object is usually encoded in the phase of a recorded fringe patte ...

2011

Implementation of optimal Galerkin and Collocation approximations of PDEs with Random Coefficients

Fabio Nobile, Lorenzo Tamellini

In this work we first focus on the Stochastic Galerkin approximation of the solution u of an elliptic stochastic PDE. We rely on sharp estimates for the decay of the coefficients of the spectral expansion of u on orthogonal polynomials to build a sequence ...

2011

Fast O(1) Bilateral Filtering Using Trigonometric Range Kernels

Michaël Unser, Daniel Sage, Kunal Narayan Chaudhury

It is well known that spatial averaging can be realized (in space or frequency domain) using algorithms whose complexity does not scale with the size or shape of the filter. These fast algorithms are generally referred to as constant-time or O(1) algorithm ...

IEEE2011

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