Remarks on variational characterizations of eigenvalues and \(n\)-width problems
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.
scientific article; zbMATH DE number 3554988