Remarks on variational characterizations of eigenvalues and \(n\)-width problems
type: Item
instance of: scholarly article
title: Remarks on variational characterizations of eigenvalues and \(n\)-width problems
zbMATH Open document ID: 0356.49027
DOI: 10.1016/0022-247X(76)90148-7
author: L. A. Karlovitz
published in: Journal of Mathematical Analysis and Applications
publication date: 1976-01-01T00:00:00Z
review text: The author investigates classical variational problems by studying the set of extremal subspaces, i.e., subspaces for which the extreme value is attained. The problems treated are the variational characterization of eigenvalues and Kolmogorov \(n\)-width problems. The interrelation between these problems is emphasized with specific focus on their geometric and approximation theoretical aspects. It is demonstrated that the non-uniqueness of the classical choice in \(n\)-width problems is more useful than the one in the variational characterization of eigenvalues. Here the non-uniqueness can be used to select an extremal subspace in a numerically advantageous manner so that the error between the actual and approximate solutions is minimized.
Mathematics Subject Classification ID: 49Q20
zbMATH DE Number: 3554988
MaRDI profile type: Publication
cites work: Q4769567
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description: scientific article; zbMATH DE number 3554988