Optimal approximation of linear operators: a singular value decomposition approach

H.B. Siahaan, S. Weiland, A.A. Stoorvogel

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

Abstract

The purpose of this paper is to propose a definition of a set of singular values and a singular value decomposition associated with a linear operator defined on arbitrary normed linear spaces. This generalizes the usual notion of singular values and singular value decompositions to operators defined on spaces equipped with the p-norm, where p is arbitrary. Basic properties of these generalized singular values are derived and the problem of optimal rank approximation of linear operators is investigated in this context. We give sufficient conditions for the existence of optimal rank approximants in the p-induced norm and discuss an application of generalized singular values for the identification of dynamical systems from data.
Original languageEnglish
Title of host publicationProceedings 15th International Symposium on Mathematical Theory of Networks and Systems (MNTS'02, Notre Dame IN, USA, August 12-16, 2002), Session FM3
EditorsD.S. Gilliam, J. Rosenthal
Place of PublicationNotre Dame IN, USA
PublisherUniv. Notre Dame
Pages580-590
Publication statusPublished - 2002

Fingerprint

Dive into the research topics of 'Optimal approximation of linear operators: a singular value decomposition approach'. Together they form a unique fingerprint.

Cite this