Displaying similar documents to “Remarks on optimum kernels and optimum boundary kernels”

Characterization of collision kernels

Laurent Desvillettes, Francesco Salvarani (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper we show how abstract physical requirements are enough to characterize the classical collision kernels appearing in kinetic equations. In particular Boltzmann and Landau kernels are derived.

A kernel-based learning algorithm combining kernel discriminant coordinates and kernel principal components

Karol Deręgowski, Mirosław Krzyśko (2014)

Biometrical Letters

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Kernel principal components (KPC) and kernel discriminant coordinates (KDC), which are the extensions of principal components and discriminant coordinates, respectively, from a linear domain to a nonlinear domain via the kernel trick, are two very popular nonlinear feature extraction methods. The kernel discriminant coordinates space has proven to be a very powerful space for pattern recognition. However, further study shows that there are still drawbacks in this method. To improve the...

Optimal asymptotic estimates for the volume of internal inhomogeneities in terms of multiple boundary measurements

Yves Capdeboscq, Michael S. Vogelius (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We recently derived a very general representation formula for the boundary voltage perturbations caused by internal conductivity inhomogeneities of low volume fraction (cf. Capdeboscq and Vogelius (2003)). In this paper we show how this representation formula may be used to obtain very accurate estimates for the size of the inhomogeneities in terms of multiple boundary measurements. As demonstrated by our computational experiments, these estimates are significantly better than previously...