Representations and bounds for zeros of orthogonal polynomials and eigenvalues of sign-symmetric tri-diagonal matrices

Erik A. van Doorn

    Research output: Contribution to journalArticleAcademic

    35 Citations (Scopus)
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    Abstract

    We consider a sequence ¦pn¦ of orthogonal polynomials defined by a three-term recurrence formula. Representations and bounds are derived for the endpoints of the smallest interval containing the (real and distinct) zeros of Pn in terms of the parameters in the recurrence relation. These results are brought to light by viewing (−1)nPn as the characteristic polynomial of a sign-symmetric tri-diagonal matrix of order n. Our findings are subsequently used to obtain new proofs for a number of bounds on the endpoints of the true and limit intervals of orthogonality for the sequence ¦pn¦.
    Original languageEnglish
    Pages (from-to)254-266
    JournalJournal of approximation theory
    Volume51
    Issue number3
    DOIs
    Publication statusPublished - 1987

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