English  |  正體中文  |  简体中文  |  全文筆數/總筆數 : 51772/86996 (60%)
造訪人次 : 8375856      線上人數 : 62
RC Version 7.0 © Powered By DSPACE, MIT. Enhanced by NTU Library & TKU Library IR team.
搜尋範圍 查詢小技巧:
  • 您可在西文檢索詞彙前後加上"雙引號",以獲取較精準的檢索結果
  • 若欲以作者姓名搜尋,建議至進階搜尋限定作者欄位,可獲得較完整資料
  • 進階搜尋
    請使用永久網址來引用或連結此文件: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/41397

    題名: Linear equations over cones and Collatz-Wielandt numbers
    作者: Tam, Bit-Shun;Schneider, Hans
    貢獻者: 淡江大學數學學系
    關鍵詞: Cone-preserving map;Perron–Frobenius theory;Local spectral radius;Local Perron–Schaefer condition;Nonnegative matrix;Collatz–Wielandt number;Collatz–Wielandt set;Alternating sequence
    日期: 2003-04
    上傳時間: 2013-06-13 11:24:48 (UTC+8)
    出版者: Philadelphia: Elsevier Inc.
    摘要: Let K be a proper cone in , let A be an n×n real matrix that satisfies AK⊆K, let b be a given vector of K, and let λ be a given positive real number. The following two linear equations are considered in this paper: (i) , and (ii) (A−λIn)x=b, x∈K. We obtain several equivalent conditions for the solvability of the first equation. For the second equation we give an equivalent condition for its solvability in case when λ>ρb(A), and we also find a necessary condition when λ=ρb(A) and also when λ<ρb(A), sufficiently close to ρb(A), where ρb(A) denotes the local spectral radius of A at b. With λ fixed, we also consider the questions of when the set (A−λIn)K∩K equals {0} or K, and what the face of K generated by the set is. Then we derive some new results about local spectral radii and Collatz–Wielandt sets (or numbers) associated with a cone-preserving map, and extend a known characterization of M-matrices among Z-matrices in terms of alternating sequences.
    關聯: Linear Algebra and Its Applications 363, pp.295-332
    DOI: 10.1016/S0024-3795(01)00565-1
    顯示於類別:[數學學系暨研究所] 期刊論文


    檔案 大小格式瀏覽次數
    0024-3795_363p.295-332.pdf326KbAdobe PDF103檢視/開啟



    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library & TKU Library IR teams. Copyright ©   - 回饋