Optimal approximation of linear operators: a singular value decomposition approach

Hardy B. Siahaan, Siep Weiland, Antonie Arij Stoorvogel

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    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 languageUndefined
    Pages15651
    Number of pages11
    Publication statusPublished - Aug 2002
    Event15th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2002 - University of Notre Dame, Notre Dame, United States
    Duration: 12 Aug 200216 Aug 2002
    Conference number: 15

    Conference

    Conference15th International Symposium on Mathematical Theory of Networks and Systems, MTNS 2002
    Abbreviated titleMTNS 2002
    CountryUnited States
    CityNotre Dame
    Period12/08/0216/08/02

    Keywords

    • Linear systems
    • EWI-16648
    • Singular values
    • Optimalidentification
    • Rank reduction
    • Optimal approximation
    • IR-69043

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