| dc.contributor.advisor | 蔡炎龍 | zh_TW |
| dc.contributor.advisor | Tsai, Yen Lung | en_US |
| dc.contributor.author (Authors) | 游竣博 | zh_TW |
| dc.contributor.author (Authors) | You, Jiun Bo | en_US |
| dc.creator (作者) | 游竣博 | zh_TW |
| dc.creator (作者) | You, Jiun Bo | en_US |
| dc.date (日期) | 2011 | en_US |
| dc.date.accessioned | 17-Apr-2012 10:25:01 (UTC+8) | - |
| dc.date.available | 17-Apr-2012 10:25:01 (UTC+8) | - |
| dc.date.issued (上傳時間) | 17-Apr-2012 10:25:01 (UTC+8) | - |
| dc.identifier (Other Identifiers) | G0098751001 | en_US |
| dc.identifier.uri (URI) | http://nccur.lib.nccu.edu.tw/handle/140.119/52849 | - |
| dc.description (描述) | 碩士 | zh_TW |
| dc.description (描述) | 國立政治大學 | zh_TW |
| dc.description (描述) | 應用數學研究所 | zh_TW |
| dc.description (描述) | 98751001 | zh_TW |
| dc.description (描述) | 100 | zh_TW |
| dc.description.abstract (摘要) | 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。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。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)。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 (摘要) | 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.As 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.The 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.Finally, we will use MATLAB to solve tropical linear systems of these two types. | en_US |
| dc.description.tableofcontents | Abstract ... i中文摘要 ... ii目錄 ... iii第一章 緒論 ... 1第二章 基本介紹 ... 4第三章 熱帶線性系統 A x = b ... 10 第一節 問題求解 ... 10 第二節 演算法及例子 ... 12第四章 雙邊齊次熱帶線性系統 A x = B y ... 15 第一節 問題求解 ... 15 第二節 演算法及例子 ... 23第五章 結論 ... 27附錄 ... 28參考文獻 ... 49 | zh_TW |
| dc.language.iso | en_US | - |
| dc.source.uri (資料來源) | http://thesis.lib.nccu.edu.tw/record/#G0098751001 | en_US |
| dc.subject (關鍵詞) | 熱帶線性系統 | zh_TW |
| dc.subject (關鍵詞) | tropical linear system | en_US |
| dc.title (題名) | 熱帶線性系統之研究 | zh_TW |
| dc.title (題名) | On tropical linear systems | en_US |
| dc.type (資料類型) | thesis | en |
| dc.relation.reference (參考文獻) | [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 (參考文獻) | [2] Diane Maclagan and Bernd Sturmfels. Introduction to tropical geometry, Nov 2009. 1 | zh_TW |
| dc.relation.reference (參考文獻) | [3] Grigory Mikhalkin. Tropical geometry and its applications, May 2006. 1 | zh_TW |
| dc.relation.reference (參考文獻) | [4] J{\\"{u}}rgen Richter-Gebert, Bernd Sturmfels, and Thorsten Theobald. First steps in tropical geometry, Dec 2003. 1 | zh_TW |
| dc.relation.reference (參考文獻) | [5] David Speyer and Bernd Sturmfels. Tropical mathematics, Aug 2004. 1 | zh_TW |
| dc.relation.reference (參考文獻) | [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 (參考文獻) | [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 (參考文獻) | [8] Stephen H. Friedberg, Arnold J. Insel, and Lawrence E. Spence. Linear algebra, Jul 2003. 3 | zh_TW |
| dc.relation.reference (參考文獻) | [9] MathWorks. http://www.mathworks.com/products/matlab/. 27 | zh_TW |
| dc.relation.reference (參考文獻) | [10] 張智星. Matlab 程式設計與應用, Sep 2000. 27 | zh_TW |
| dc.relation.reference (參考文獻) | [11] David Fass. http://www.mathworks.com/matlabcentral/ leexchange/5475-cartprod-cartesian-product-of-multiple-sets, Jul 2004. 40 | zh_TW |
| dc.relation.reference (參考文獻) | [12] David Fass. http://www.mathworks.com/matlabcentral/ leexchange/5476-ind2subvect-multiple-subscript-vector-from-linear-index, Jul 2004. 42 | zh_TW |
