本文選題：算法 + 特征值��； 參考：《河北師范大學》2015年碩士論文

【摘要】：極大加代數(shù)是研究系統(tǒng)科學的一個重要工具,它可使時序離散事件系統(tǒng)具有像一般線性系統(tǒng)那樣的狀態(tài)空間表達式,達到利用線性系統(tǒng)模型分析離散事件動態(tài)系統(tǒng)的目的.極大加代數(shù)能解決許多實際問題,例如,資源分配問題,鐵路系統(tǒng)調(diào)度問題,生產(chǎn)流水線最優(yōu)控制問題,制造系統(tǒng)優(yōu)化和控制問題等.在極大加代數(shù)結(jié)構(gòu)中重新定義了許多重要的數(shù)學概念,并討論其性質(zhì),例如,極大加代數(shù)矩陣的行列式及其性質(zhì)、極大加代數(shù)矩陣的特征值和特征向量、線性獨立、模結(jié)構(gòu)等.矩陣的特征問題和像問題是極大加代數(shù)中重要的數(shù)學概念且有著重要的理論和實踐意義.特征值表示系統(tǒng)的周期時間,特征向量表示系統(tǒng)的穩(wěn)定狀態(tài).像表示系統(tǒng)的運行結(jié)果.本文的主要內(nèi)容是在前人工作的基礎(chǔ)上,研究極大加代數(shù)矩陣的整特征向量和整像.給出可約極大加代數(shù)矩陣存在塊整特征向量的充分必要條件和在一定條件下存在整特征向量的充分必要條件.給出廣義整像算法,數(shù)值例子表明廣義整像算法是偽多項式算法.給出??×3極大加代數(shù)矩陣和Monge矩陣存在整像的充分必要條件,并且給出強確定矩陣存在整特征向量和存在整像的等價性.本文共分為五個部分.引言部分,介紹與極大加代數(shù)矩陣整特征向量和整像相關(guān)的研究背景和研究現(xiàn)狀.第一章,介紹本文涉及到的基本概念和引理,包括極大加代數(shù)、可約極大加代數(shù)矩陣、特征值、特征向量、整像等.舉例說明極大加代數(shù)矩陣間的運算.這些概念和引理為后面的章節(jié)提供了理論支撐.第二章,介紹極大加代數(shù)矩陣的整特征向量.提出塊整特征向量的概念,分別給出可約極大加代數(shù)矩陣存在塊整特征向量的充分必要條件和在一定條件下存在整特征向量的充分必要條件并給出相應(yīng)的數(shù)值例子.第三章,介紹極大加代數(shù)矩陣的整像.給出??×3極大加代數(shù)矩陣存在整像的充分必要條件,??×??極大加代數(shù)矩陣特殊條件下存在整像的充分必要條件.給出廣義整像算法,通過驗證主對角線上的塊極大加代數(shù)矩陣確定可約和不可約極大加代數(shù)矩陣的整特征向量.數(shù)值例子表明廣義整像算法是偽多項式算法.最后給出Monge矩陣存在整像的充分必要條件和強確定矩陣存在整特征向量和存在整像的等價性.結(jié)論部分,總結(jié)本篇論文的主要結(jié)論,并提出有待進一步研究的問題.
[Abstract]:The maximum additive algebra is an important tool for the study of system science. It can make the time series discrete event system have the state space expression like the general linear system, and achieve the purpose of analyzing the discrete event dynamic system by using the linear system model. The problem of unified scheduling, optimal control of production lines, optimization and control of manufacturing systems, and so on. Many important mathematical concepts are redefined in the maximal additive algebraic structure, and its properties are discussed, such as the determinant and its properties of the maximal additive algebraic matrix, the eigenvalues and eigenvectors of the maximal additive number matrix, linear independence, and the model knot. The characteristic problems and image problems of matrices are important mathematical concepts in maximal addition algebra and have important theoretical and practical significance. The eigenvalues represent the periodic time of the system, the eigenvectors represent the stable state of the system. The full and necessary conditions for the existence of integral eigenvectors of an algebraic matrix with an algebraic matrix and the sufficient and necessary conditions for the existence of an integral eigenvector under certain conditions are given. The generalized integer image algorithm is given, and the numerical example shows that the generalized integer image algorithm is a pseudo multi term algorithm. The?? * 3 maximal additive algebraic matrix is given. The sufficient and necessary conditions for the existence of an integer image with the Monge matrix and the equivalence of the existence of an integer eigenvector and the existence of an integer image are given. This paper is divided into five parts. The introduction part introduces the research background and research status related to the integral eigenvector and integer image of the maximal additive algebra. Chapter 1 introduces the basic probability of this article. The idea and lemma, including the maximal addition of algebra, can be greatly added to the algebraic matrix, eigenvalues, eigenvectors, and integer images. Examples are given to illustrate the operations between the maximal added algebraic matrices. These concepts and lemmas provide theoretical support for the subsequent chapters. The second chapter introduces the entire eigenvector of the maximal additive algebraic matrix. The sufficient and necessary conditions for the existence of integral eigenvectors of the approximately maximal additive algebraic matrices and the sufficient and necessary conditions for the existence of an integral eigenvector under certain conditions are given and the corresponding numerical examples are given. In the third chapter, the entire image of the maximal additive algebraic matrix is introduced. The generalized integer image algorithm is given. The generalized integer image algorithm is given, and the integral eigenvector of the reducible and irreducible algebraic matrix is determined by verifying the maximal addition algebraic matrix of the block on the main diagonal line. The numerical example shows that the generalized integer image algorithm is a pseudo multi term algorithm. Finally, the existence of the Monge matrix is given. The sufficient and necessary conditions of the image and the equivalence of the integral eigenvector and the existence of the whole image exist in the sufficient and necessary condition of the image and the strong deterministic matrix.
【學位授予單位】：河北師范大學
【學位級別】：碩士
【學位授予年份】：2015
【分類號】：O151.21

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相關(guān)期刊論文 前1條

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本文編號：1928256