[Dottorcomp] Seminari di Matematica Applicata. Martedì 17 maggio. Espen Sande.

[Stefano Lisini]

Seminari di Matematica Applicata, Dipartimento di Matematica "F.
Casorati" e Istituto del CNR IMATI "E. Magenes" di Pavia.

Martedì 17 maggio 2022, alle ore 17.00 precise, presso l'aula Beltrami
del Dipartimento di Matematica,

Espen Sande (EPFL)terrà un seminario dal titolo:

Best low-rank approximations and Kolmogorov n-width

Il seminario verrà anche trasmesso in diretta su zoom al link

https://us02web.zoom.us/j/87518137128?pwd=eHg2eG9QZUdydFJEU1NESWN5a1lPQT09

ID riunione: 875 1813 7128
Passcode: 880047

Abstract.
It is well known that if the singular values of a matrix A are distinct,
then the best rank-n approximation to A is uniquely determined in the
Frobenius norm and given by the truncated singular value decomposition. On
the other hand, this uniqueness is in general not true for best rank-n
approximations in the spectral norm. In this talk we relate the problem of
finding best rank-n approximations in the spectral norm to Kolmogorov
n-widths and corresponding optimal spaces. By providing new criteria for
optimality of subspaces with respect to the n-width, we describe a large
family of best rank-n approximations to A. This results in a variety of
solutions to the best low-rank approximation problem and provides
alternatives to the truncated singular value decomposition. This variety
can be exploited to obtain best low-rank approximations with
problem-oriented properties. Special attention is paid to the case of
rank-1 approximation.
We further discuss the generalization of these results to compact operators
in L^2, and explain how they can be used to describe the out-performance of
smooth spline approximations of differential equations (so-called
k-refinement in isogeometric analysis) when compared to classical finite
element methods.
This talk is based on joint work with Michael S. Floater, Carla Manni and
Hendrik Speleers.
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Pagina web dei Seminari di Matematica Applicata
https://matematica.unipv.it/ricerca/cicli-di-seminari/seminari-di-matematica-applicata/
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