| 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 | en |
| ISSN | 0024-3795 |
| 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 | USA |
| 公開徵稿 | |
| 出版型式 | 紙本 |
| 相關連結 |
機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/41397 ) |
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