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Convergence Rates of the POD–Greedy Method

Bernard Haasdonk (2013)

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

Iterative approximation algorithms are successfully applied in parametric approximation tasks. In particular, reduced basis methods make use of the so-called Greedy algorithm for approximating solution sets of parametrized partial differential equations. Recently, a priori convergence rate statements for this algorithm have been given (Buffa et al. 2009, Binev et al. 2010). The goal of the current study is the extension to time-dependent problems, which are typically approximated using the POD–Greedy...

How many are affine connections with torsion

Zdeněk Dušek, Oldřich Kowalski (2014)

Archivum Mathematicum

The question how many real analytic affine connections exist locally on a smooth manifold M of dimension n is studied. The families of general affine connections with torsion and with skew-symmetric Ricci tensor, or symmetric Ricci tensor, respectively, are described in terms of the number of arbitrary functions of n variables.

How many are equiaffine connections with torsion

Zdeněk Dušek, Oldřich Kowalski (2015)

Archivum Mathematicum

The question how many real analytic equiaffine connections with arbitrary torsion exist locally on a smooth manifold M of dimension n is studied. The families of general equiaffine connections and with skew-symmetric Ricci tensor, or with symmetric Ricci tensor, respectively, are described in terms of the number of arbitrary functions of n variables.

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