On the Collatz-Wielandt sets associated with a cone-preserving map

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題名:	On the Collatz-Wielandt sets associated with a cone-preserving map
作者:	Tam, Bit-Shun;Wu, Shiow-Fang
貢獻者:	淡江大學數學學系
日期:	1989-12
上傳時間:	2013-06-13 11:25:21 (UTC+8)
出版者:	Philadelphia: Elsevier Inc.
摘要:	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
關聯:	Linear Algebra and Its Applications 125(C), pp.77-95
DOI:	10.1016/0024-3795(89)90033-5
顯示於類別:	[數學學系暨研究所] 期刊論文

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