10,810 research outputs found
Incompressible Navier-Stokes-Fourier Limit from The Boltzmann Equation: Classical Solutions
The global classical solution to the incompressible Navier-Stokes-Fourier
equation with small initial data in the whole space is constructed through a
zero Knudsen number limit from the solutions to the Boltzmann equation with
general collision kernels. The key point is the uniform estimate of the Sobolev
norm on the global solutions to the Boltzmann equation.Comment: 21 page
Geometric methods for estimation of structured covariances
We consider problems of estimation of structured covariance matrices, and in
particular of matrices with a Toeplitz structure. We follow a geometric
viewpoint that is based on some suitable notion of distance. To this end, we
overview and compare several alternatives metrics and divergence measures. We
advocate a specific one which represents the Wasserstein distance between the
corresponding Gaussians distributions and show that it coincides with the
so-called Bures/Hellinger distance between covariance matrices as well. Most
importantly, besides the physically appealing interpretation, computation of
the metric requires solving a linear matrix inequality (LMI). As a consequence,
computations scale nicely for problems involving large covariance matrices, and
linear prior constraints on the covariance structure are easy to handle. We
compare this transportation/Bures/Hellinger metric with the maximum likelihood
and the Burg methods as to their performance with regard to estimation of power
spectra with spectral lines on a representative case study from the literature.Comment: 12 pages, 3 figure
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