Please use this identifier to cite or link to this item:
https://ah.lib.nccu.edu.tw/handle/140.119/52849
DC Field | Value | Language |
---|---|---|
dc.contributor.advisor | 蔡炎龍 | zh_TW |
dc.contributor.advisor | Tsai, Yen Lung | en_US |
dc.contributor.author | 游竣博 | zh_TW |
dc.contributor.author | You, Jiun Bo | en_US |
dc.creator | 游竣博 | zh_TW |
dc.creator | You, Jiun Bo | en_US |
dc.date | 2011 | en_US |
dc.date.accessioned | 2012-04-17T02:25:01Z | - |
dc.date.available | 2012-04-17T02:25:01Z | - |
dc.date.issued | 2012-04-17T02:25:01Z | - |
dc.identifier | G0098751001 | en_US |
dc.identifier.uri | http://nccur.lib.nccu.edu.tw/handle/140.119/52849 | - |
dc.description | 碩士 | zh_TW |
dc.description | 國立政治大學 | zh_TW |
dc.description | 應用數學研究所 | zh_TW |
dc.description | 98751001 | zh_TW |
dc.description | 100 | zh_TW |
dc.description.abstract | 本篇論文主要在探討熱帶線性系統(tropical linear system) A x = b 與雙邊齊次熱帶線性系統(two-sided homogeneous tropical linear system) A x = B y 的求解方法。我們將明確的描述任何熱帶線性系統與雙邊齊次熱帶線性系統的解。\n\n如同古典的論述, 當求解線性系統 A x = b 時, 我們首先會先找到對應的 ""齊次`` 系統 A x = 0 來求解。而對於雙邊齊次熱帶線性系統, 我們將利用勝序列的概念, 將雙邊齊次熱帶線性系統轉化為 k 組古典熱帶線性系統: 含等式系統 S: C[x^t -y^t 1]^t = 0 與不等式系統 T: D[x^t -y^t 1]^t <= 0 。除此之外, 利用相容性條件來減少 k 的數量。\n\n過程中我們處理的 S, T 均為雙變量的系統, 係數分別為 1 與 -1, 對於 S 我們以高斯-喬登消去法(Gauss–Jordan elimination)處理。對於 T 我們將以類似高斯-喬登消去法的方式進行列運算, 因此我們定義次特殊矩陣(sub-special matrix), 而進行的過程我們稱之為次特殊化(sub–specialization)。\n\n最後將以 MATLAB 作為工具來求解出這兩類的熱帶線性系統。 | zh_TW |
dc.description.abstract | The thesis mainly discusses the methods of finding solutions of tropical linear systems A x = b and two-sided homogeneous tropical linear systems A x = B y. We are able to give explicit descriptions of all solutions of any tropical linear systems A x = b and two-sided homogeneous tropical linear systems A x = B y.\n\nAs the classical situations, when solving the linear systems of the form A x = b, we first find the solutions for the corresponding ""homogeneous`` case A x = 0. For two-sided homogeneous tropical linear systems A x = B y, we use the concept of win sequence to convert it into a finite number k of classical linear systems: either a system S: C[x^t -y^t 1]^t = 0 of equations or a system T: D[x^t -y^t 1]^t <= 0 of inequalities. Moreover, we used so called ""compatibility conditions`` to reduce the number of k.\n\nThe particular feature of both S and T is that each item (equation or inequality) is bivariate. It involves exactly two variables; one variable with coefficient 1, and the other one with -1. S is solved by Gauss-Jordon elimination. We explain how to solve T by a method similar to Gauss-Jordon elimination. To achieve this, we introduce the notion of sub–special matrix. The procedure applied to T is called sub–specialization.\n\nFinally, we will use MATLAB to solve tropical linear systems of these two types. | en_US |
dc.description.tableofcontents | Abstract ... i\n中文摘要 ... ii\n目錄 ... iii\n第一章 緒論 ... 1\n第二章 基本介紹 ... 4\n第三章 熱帶線性系統 A x = b ... 10\n 第一節 問題求解 ... 10\n 第二節 演算法及例子 ... 12\n第四章 雙邊齊次熱帶線性系統 A x = B y ... 15\n 第一節 問題求解 ... 15\n 第二節 演算法及例子 ... 23\n第五章 結論 ... 27\n附錄 ... 28\n參考文獻 ... 49 | zh_TW |
dc.language.iso | en_US | - |
dc.source.uri | http://thesis.lib.nccu.edu.tw/record/#G0098751001 | en_US |
dc.subject | 熱帶線性系統 | zh_TW |
dc.subject | tropical linear system | en_US |
dc.title | 熱帶線性系統之研究 | zh_TW |
dc.title | On tropical linear systems | en_US |
dc.type | thesis | en |
dc.relation.reference | [1] Fran{\\c{c}}ois Baccelli, Guy Cohen, Geert Jan Olsder, and Jean Pierre Quadrat. Synchronization and linearity-an algebra for discrete event systems, 1992. 1 | zh_TW |
dc.relation.reference | [2] Diane Maclagan and Bernd Sturmfels. Introduction to tropical geometry, Nov 2009. 1 | zh_TW |
dc.relation.reference | [3] Grigory Mikhalkin. Tropical geometry and its applications, May 2006. 1 | zh_TW |
dc.relation.reference | [4] J{\\\"{u}}rgen Richter-Gebert, Bernd Sturmfels, and Thorsten Theobald. First steps in tropical geometry, Dec 2003. 1 | zh_TW |
dc.relation.reference | [5] David Speyer and Bernd Sturmfels. Tropical mathematics, Aug 2004. 1 | zh_TW |
dc.relation.reference | [6] P. Butkovi{\\v{c}} and R.A. Cuninghame-Green. The equation A x = B y over (max, +). Theoretical Computer Science, 293(1):3-12, Feb 2003. 1, 3, 16, 24 | zh_TW |
dc.relation.reference | [7] E. Lorenzo and M. J. de la Puente. An algorithm to describe the solution set of any tropical linear system A x = B x, jul 2010. 1, 3 | zh_TW |
dc.relation.reference | [8] Stephen H. Friedberg, Arnold J. Insel, and Lawrence E. Spence. Linear algebra, Jul 2003. 3 | zh_TW |
dc.relation.reference | [9] MathWorks. http://www.mathworks.com/products/matlab/. 27 | zh_TW |
dc.relation.reference | [10] 張智星. Matlab 程式設計與應用, Sep 2000. 27 | zh_TW |
dc.relation.reference | [11] David Fass. http://www.mathworks.com/matlabcentral/ leexchange/5475-cartprod-cartesian-product-of-multiple-sets, Jul 2004. 40 | zh_TW |
dc.relation.reference | [12] David Fass. http://www.mathworks.com/matlabcentral/ leexchange/5476-ind2subvect-multiple-subscript-vector-from-linear-index, Jul 2004. 42 | zh_TW |
item.fulltext | With Fulltext | - |
item.cerifentitytype | Publications | - |
item.openairecristype | http://purl.org/coar/resource_type/c_46ec | - |
item.grantfulltext | open | - |
item.openairetype | thesis | - |
item.languageiso639-1 | en_US | - |
Appears in Collections: | 學位論文 |
Files in This Item:
File | Size | Format | |
---|---|---|---|
100101.pdf | 893.19 kB | Adobe PDF2 | View/Open |
Google ScholarTM
Check
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.