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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...

Convexity on the space of Kähler metrics

Bo Berndtsson (2013)

Annales de la faculté des sciences de Toulouse Mathématiques

These are the lecture notes of a minicourse given at a winter school in Marseille 2011. The aim of the course was to give an introduction to recent work on the geometry of the space of Kähler metrics associated to an ample line bundle. The emphasis of the course was the role of convexity, both as a motivating example and as a tool.

Coomologia di un campo vettoriale mai nullo

Angela De Sanctis, Giuliano Sorani (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We write a cohomological resolution of the sheaf 𝒮 of solutions of the differential operator / x n on a manifold M and study the cohomology groups H 0 ( M , 𝒮 ) and H 1 ( M , 𝒮 ) .

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