Displaying similar documents to “Finding the principal points of a random variable”

Méthodes géométriques et analytiques pour étudier l'application exponentielle, la sphère et le front d'onde en géométrie sous-riemannienne dans le cas Martinet

Bernard Bonnard, Monique Chyba (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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Consider a sub-riemannian geometry (U,D,g) where U is a neighborhood of 0 in R 3, D is a Martinet type distribution identified to ker ω, ω being the 1-form: ω = d z - y 2 2 d x , q=(x,y,z) and g is a metric on D which can be taken in the normal form:...

Exponential convergence of quadrature for integral operators with Gevrey kernels

Alexey Chernov, Tobias von Petersdorff, Christoph Schwab (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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Galerkin discretizations of integral equations in ℝ d require the evaluation of integrals I = ∫ S ( 1 ) ∫ S ( 2 ) g ( x , y ) d y d x where , are -simplices and has a singularity at = . We assume that is Gevrey smooth for ≠ and satisfies bounds for the derivatives which allow algebraic singularities at = . This holds for kernel functions commonly occurring in integral equations. We construct a family of quadrature rules 𝒬 N using function evaluations of which...

Exponential convergence of quadrature for integral operators with Gevrey kernels

Alexey Chernov, Tobias von Petersdorff, Christoph Schwab (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

Similarity:

Galerkin discretizations of integral equations in ℝ d require the evaluation of integrals I = ∫ S ( 1 ) ∫ S ( 2 ) g ( x , y ) d y d x where , are -simplices and has a singularity at = . We assume that is Gevrey smooth for ≠ and satisfies bounds for the derivatives which allow algebraic singularities at = . This holds for kernel functions commonly occurring in integral equations. We construct a family of quadrature rules 𝒬 N using function evaluations of which...