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    Please use this identifier to cite or link to this item: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/41377


    Title: On the Collatz-Wielandt sets associated with a cone-preserving map
    Authors: Tam, Bit-Shun;Wu, Shiow-Fang
    Contributors: 淡江大學數學學系
    Date: 1989-12
    Issue Date: 2013-06-13 11:25:21 (UTC+8)
    Publisher: Philadelphia: Elsevier Inc.
    Abstract: Let K be a closed, pointed, full cone in Rn. In their treatment of Perron-Frobenius theory for a linear map A preserving K by Wielandt's approach, Barker and Schneider introduced four sets, namely, Ω, Ω1, Σ, and Σ1, the Collatz-Wielandt sets associated with A. We determine the greatest lower bound and the least upper bound of these sets. Some known results for a nonnegative matrix relating its spectral radius to its upper and lower Collatz-Wielandt number are extended to the setting of a cone-preserving map. Applications of our results to the nonnegativity of solutions of linear inequalities associated with a nonnegative matrix are also considered
    Relation: Linear Algebra and Its Applications 125(C), pp.77-95
    DOI: 10.1016/0024-3795(89)90033-5
    Appears in Collections:[數學學系暨研究所] 期刊論文

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