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Finite sections: A functional analytic perspective on approximation methods
Publikationstyp
Journal Article
Date Issued
2018-09
Sprache
English
Author(s)
Institut
TORE-URI
Journal
Volume
41
Issue
3
Start Page
e201800013
Citation
GAMM Mitteilungen 3 (41): e201800013- (2018-09)
Publisher DOI
Scopus ID
We review approximation methods and their stability and applicability. We then focus on the finite section method and Galerkin methods and show that on separable Hilbert spaces either one can be interpreted as the other. In the end we demonstrate that well-known methods such as the finite element method and polynomial chaos expansion are particular examples of the finite section method; their applicability can therefore be studied via the latter.