The finite section method and problems in frame theory

Ole Christensen, T. Strohmer

    Research output: Contribution to journalJournal articleResearchpeer-review

    Abstract

    The finite section method is a convenient tool for approximation of the inverse of certain operators using finite-dimensional matrix techniques. In this paper we demonstrate that the method is very useful in frame theory: it leads to an efficient approximation of the inverse frame operator and also solves related computational problems in frame theory. In the case of a frame which is localized w.r.t. an orthonormal basis we are able to estimate the rate of approximation. The results are applied to the reproducing kernel frame appearing in the theory for shift-invariant spaces generated by a Riesz basis.
    Original languageEnglish
    JournalJournal of Approximation Theory
    Volume133
    Issue number2
    Pages (from-to)221-237
    ISSN0021-9045
    DOIs
    Publication statusPublished - 2005

    Keywords

    • Localized frame
    • Finite section method
    • Frames
    • Shift-invariant system
    • Inverse frame operator

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