CHEVILLARD , Sylvain

The error function erf is a special function. It is widely used in statistical computations for instance, where it is also known as the standard normal cumulative probability. The complementary error function is defined as erfc(x)=erf(x)-1. In this paper, the computation of erf(x) and erfc(x) in arbitrary precision is detailed: our algorithms...

The evaluation of special functions often involves the evaluation of numerical constants. When the precision of the evaluation is known in advance (e.g., when developing libms) these constants are simply precomputed once and for all. In contrast, when the precision is dynamically chosen by the user (e.g., in multiple precision libraries), the...

Nous avons réalisé le bilan des émissions de gaz à effet de serre (GES) d'une équipe du centre de recherche Inria de Sophia Antipolis pour l'année 2019. L'équipe comprenait cette année-là 5 permanents, 5 doctorants, 1 post-doc, une assistante d'équipe à mi-temps et a accueilli pendant quelques mois deux stagiaires de master.

The series expansion at the origin of the Airy function Ai(x) is alternating and hence problematic to evaluate for x > 0 due to cancellation. Based on a method recently proposed by Gawronski, Müller, and Reinhard, we exhibit two functions F and G, both with nonnegative Taylor expansions at the origin, such that Ai(x) = G(x)/F(x). The sums are...

We consider dipole recovery issues from sparse magnetic data, with the use of best quadratic rational approximation techniques, together with geometrical and algebraic properties of the poles of the approximants.

We consider the inverse problem of recovering the position and moment of a magnetic dipolefrom sparse measurements of the field it generates, known on sections of three orthogonal cylindersenclosing it. This problem is motivated by recent measurements performed on Moon rocks, in viewof determining their magnetic properties. The key ingredient...

We derive some lower bounds in rational approximation of given degree to functions in the Hardy space $H^2$ of the disk. We apply these to asymptotic errors rates in approximation to Blaschke products and to Cauchy integrals on geodesic arcs.We also explain how to compute such bounds, either using Adamjan-Arov-Krein theory or linearized errors,...

In geosciences and paleomagnetism, estimating the remanent magnetization in old rocks is an important issue to study past evolution of the Earth and other planets or bodies. However, the magnetization cannot be directly measured and only the magnetic field that it produces can be recorded.In this paper we consider the case of thin samples, to...

In this work, we characterize transfer functions that can be realized with standard electronic components in linearized form, e.g. those commonly used in the design of analog amplifiers (including transmission lines) in the small signal regime. We define the stability of such transfer functions in connection with scattering theory, i.e. in...

This work takes its roots in the inverse magnetization problem, where the magnetization properties of rocks are sought from measurements of the magnetic field they generate, taken on a horizontal plane at some height above the rocks. The Poisson kernel being at the core of the corresponding magnetic potential, double integrals of functions over...

International audience

We study the properties of electronic circuits after linearization around a fixed operating point in the context of closed-loop stability analysis. When distributed elements, like transmission lines, are present in the circuit it is known that unstable circuits can be created without poles in the complex right half-plane. This undermines...

Performing a stability analysis during the design of any electronic circuit is critical to guarantee its correct operation. A closed-loop stability analysis can be performed by analysing the impedance presented by the circuit at a well-chosen node without internal access to the simulator. If any of the poles of this impedance lie in the complex...

Scanning magnetic microscopes typically measure the vertical component B_3 of the magnetic field on a horizontal rectangular grid at close proximity to the sample. This feature makes them valuable instruments for analyzing magnetized materials at fine spatial scales, e.g., in geosciences to access ancient magnetic records that might be...

We consider the inverse problem in magnetostatics for recovering the moment of a planar magnetization from measurements of the normal component of the magnetic field at a distance from the support. Such issues arise in studies of magnetic material in general and in paleomagnetism in particular. Assuming the magnetization is a measure with...

Nonlinear hyper-frequency amplifiers contain nonlinear active components and lines, that can be seen as linear infinite dimensional systems inducing delays that cannot be neglected at high frequencies. Computer assisted design tools are extensively used. They provide frequency responses but fail to provide a reliable estimation of their...