Exponential convergence of hp quadrature  for integral operators with Gevrey kernels

Alexey Chernov; Tobias von Petersdorff; Christoph Schwab

Displaying similar documents to “Exponential convergence of hp quadrature for integral operators with Gevrey kernels”

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 $I = \int_{S^{(1)}} \int_{S^{(2)}} g (x, y) d y d x$ where , are -simplices and has a singularity at = . We assume that is Gevrey smooth for $\neq$ 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...

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: $ω = d z - \frac{y^{2}}{2} d x$ , q=(x,y,z) and g is a metric on D which can be taken in the normal form:...

Towards parametrizing word equations

H. Abdulrab, P. Goralčík, G. S. Makanin (2010)

RAIRO - Theoretical Informatics and Applications

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Classically, in order to resolve an equation ≈ over a free monoid *, we reduce it by a suitable family $ℱ$ of substitutions to a family of equations ≈ , $f \in ℱ$ , each involving less variables than ≈ , and then combine solutions of ≈ into solutions of ≈ . The problem is to get $ℱ$ in a handy form. The method we propose consists in parametrizing the path traces in the so called associated to ≈ . We carry out such a parametrization in the case the prime equations in the graph involve at...