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題 名 | 以廣義反矩陣的特性推導路徑非負流量之研究=A Study of Estimating Nonnegative Path Flow by the Properties of Generalized Inverse Matrix |
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作 者 | 卓訓榮; 羅仕京; | 書刊名 | 運輸學刊 |
卷 期 | 11:2 1999.06[民88.06] |
頁 次 | 頁39-47 |
分類號 | 557.16 |
關鍵詞 | 廣義反矩陣; 正路徑流量; 均衡路網指派; Generalized inverse matrix; Positive path flow; Equilibrium network assignment; |
語 文 | 中文(Chinese) |
中文摘要 | 路段與路徑之關係可以用路段╱路徑投引矩陣(Arc/Path incidence matrix)表 示記為 △,而路段與路徑流量分別以 f 與 h 表示,則路段流量與路徑流量之關係可表為 △h = f。當△的反矩陣存在,則路徑流量可以由 h = △�笐繈 求得。由網路的特性可知, △的反矩通常不存在。儘管如此,仍可透過廣義反矩陣的特性求出路徑流量,令△�珙� △ 之 廣義反矩陣,k 為任意向量,則路徑流量為 h= △�� f + ( I- △�牷窗^k,但是此結果無 法確定 h 為正流量。因此本研究提出一演算法,以確保可求出一組正流量解,提供相關研 究應用。 |
英文摘要 | ArC/Path incidence, matrix denoted as △=〔△ 〕where △ =1 if arc a is in path p,O otherwise. Arc flow and path flow denoted as f and h respectively. The relationship between arc flow and path flow can be shown as △h = f. If △�笐縹xists, path flow h equals to △�笐繈. Unfortunately, △�笐� does not always exist. But if △�� denoted as generalized inverse of △ and k is a column vector, then path flow can be shown as h = △�浻 +( I-△�牷� )k. In this research we will provide an algorithm to find a nonnegative path flow. |
本系統中英文摘要資訊取自各篇刊載內容。