教師資料查詢 | 類別: 期刊論文 | 教師: 譚必信 Tam Bit-shun (瀏覽個人網頁)

標題:Linear equations over cones and Collatz-Wielandt numbers
學年91
學期2
出版(發表)日期2003/04/01
作品名稱Linear equations over cones and Collatz-Wielandt numbers
作品名稱(其他語言)
著者Tam, Bit-Shun; Schneider, Hans
單位淡江大學數學學系
出版者Philadelphia: Elsevier Inc.
著錄名稱、卷期、頁數Linear Algebra and Its Applications 363, pp.295-332
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.
關鍵字Cone-preserving map;Perron–Frobenius theory;Local spectral radius;Local Perron–Schaefer condition;Nonnegative matrix;Collatz–Wielandt number;Collatz–Wielandt set;Alternating sequence
語言英文
ISSN0024-3795
期刊性質國外
收錄於SCI
產學合作
通訊作者Tam, Bit-Shun
審稿制度
國別美國
公開徵稿
出版型式紙本
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