线性代数及其在规划中的应用-英文

1星价 ¥30.2 (6.7折)

2星价￥30.2 定价￥45.0

作者：郭树理,韩丽娜主编

出版社：北京理工大学出版社

本类榜单：教材

分类：教材 > 研究生/本科/专科教材

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图文详情

ISBN：9787568239691
装帧：暂无
册数：暂无
重量：暂无
开本：32开
页数：271
出版时间：2017-04-01
条形码：9787568239691 ; 978-7-5682-3969-1

本书特色

　郭树理、韩丽娜编*的《线性代数及其在规划中的应用（英文版）》从结构上分为三个部分。读者选择上，本书适用于具有数学、工程类或者理科专业高年级学生、研究生、教师、工程师。专业选择上，本书适应于系统分析、算子研究、数值化分析、管理科学以及其他应用学科。

内容简介

全书从结构上分为三个部分。**部分主要介绍群、环、矩阵的基本理论。**章着重介绍集合、部分序、函数、单射，双射、满射以及方程的解等概念以及一些基本结论；第二章是介绍群的理论，是全书比较难的章节，也是线性代数的中心问题之一。特别环同胚映射、模同胚映射是群同胚映射的特殊情形。第二章，第三章涉及的环、矩阵等都是线性代数的中心议题。第三章主要谈环——具有乘法运算的加法群，其加法、乘法运算满足分配律。理想是正则子群，环是群的同态等。第四章主要介绍了逆矩阵，转置矩阵，初等矩阵，系统方程以及行列式的秩等。重要的结论包括相似矩阵有相同的秩，相同的迹，以及相同的特征多项式。一个有限张成的向量空间自同态有明确定义的行列式,迹和特征多项式等。第二部分包括了向量分析、张量分析中基本概念、向量空间、线性变换、矩阵的秩以及张量代数。这部分内容展示给工程类、理科类学生矢量空间，张量空间*新进展以及这些概念系统化的发展过程。这部分知识覆盖了向量空间、线性变换、矩阵的秩、张量代数，写作目的是展示工程实践中需要了解的主要概念、基本结论。第三部分主要介绍规划理论，特点如下。第十章介绍了线性规划中时变多项式算法的理论与方法，*重要的是内点法。第十一章介绍了线性规划中一些广义必要条件，例如*优问题中一阶、二阶必要条件以及不考虑导数条件下的0阶条件、非约束条件下下降法、收敛性分析、线性规划以及非线性规划中牛顿法。第十二章介绍了约束条件下线性规划必要条件的全局性理论，展示了0阶条件、一般非线性规划中的内点法、惩罚函数以及障碍函数法。本部分的一个重要特色是分别从原空间、对偶空间中展示全局或局部性结论。读者选择上，本书适用于具有数学、工程类或者理科专业高年级学生、研究生、教师、工程师。专业选择上，本书适应于系统分析、算子研究、数值化分析、管理科学以及其他应用学科。

Part ⅠChapter 1 Background and Fundamentals of Mathematics1.1 Basic Concepts1.2 Relations1.3 Functions1.4 The Integers1.4.1 Long Division1.4.2 Relatively Prime1.4.3 Prime1.4.4 The Unique Factorization TheoremChapter 2 Groups2.1 Groups2.2 Subgroups2.3 Normal Subgroups2.4 Homomorphisms2.5 Permutations2.6 Product of GroupsChapter 3 Rings3.1 Commutative Rings3.2 Units3.3 The Integers Mod N3.4 Ideals and Quotient Rings3.5 Homomorphism3.6 Polynomial Rings3.6.1 The Division Algorithm3.6.2 Associate3.7 Product of Rings3.8 Characteristic3.9 Boolean RingsChapter 4 Matrices and Matrix Rings4.1 Elementary Operations and Elementary Matrices4.2 Systems of Equations4.3 Determinants4.4 Similarity Part ⅡChapter 5 Vector Spaces5.1 The Axioms for a Vector Space5.2 Linear Independence,Dimension,and Basis5.3 Intersection,Sum and Direct Sum of Subspaces5.4 Factor Space5.5 Inner Product Spaces5.6 Orthonormal Bases and Orthogonal Complements5.7 Reciprocal Basis and Change of BasisChapter 6 Linear Transformations6.1 Definition of Linear Transformation6.2 Sums and Products of Liner Transformations6.3 Special Types of Linear Transformations6.4 The Adjoint of a Linear Transformation6.5 Component FormulasChapter 7 Determinants And Matrices7.1 The Generalized Kronecker Deltas and the Summation Convention7.2 Determinants7.3 The Matrix of a Linear Transformation7.4 Solution of Systems of Linear Equation7.5 Special MatricesChapter 8 Spectral Decompositions8.1 Direct Sum of Endomorphisms8.2 Eigenvectors and Eigenvalues8.3 The Characteristic Polynomial8.4 Spectral Decomposition for Hermitian Endomorphisms8.5 Illustrative Examples8.6 The Minimal Polynomial8.7 Spectral Decomposition for Arbitrary EndomorphismsChapter 9 Tensor Algebra9.1 Linear Functions,the Dual Space9.2 The Second Dual Space, Canonical Isomorphisms Part Ⅲ Chapter 10 Linear Programming10.1 Basic Properties of Linear Programs10.2 Many Computational Procedures to Simplex Method10.3 Duality10.3.1 Dual Linear Programs10.3.2 The Duality Theorem10.3.3 Relations to the Simplex Procedure10.4 Interior-point Methods10.4.1 Elements of Complexity Theory10.4.2 The Analytic Center10.4.3 The Central Path10.4.4 Solution StrategiesChapter 11 Unconstrained Problems11.1 Transportation and Network Flow Problems11.1.1 The Transportation Problem11.1.2 The Northwest Comer Rule11.1.3 Basic Network Concepts11.1.4 Maximal Flow11.2 Basic Properties of Solutions and Algorithms11.2.1 First-order Necessary Conditions11.2.2 Second-order Conditions11.2.3 Minimization and Maximization of Convex Functions11.2.4 Zeroth-order Conditions11.2.5 Global Convergence of Descent Algorithms11.2.6 Speed of Convergence11.3 Basic Descent Methods11.3.1 Fibonacci and Golden Section Search11.3.2 Closedness of Line Search Algorithms11.3.3 Line Search11.3.4 The Steepest Descent Method11.3.5 Coordinate Descent Methods11.4 Conjugate Direction Methods11.4.1 Conjugate Directions11.4.2 Descent Properties of the Conjugate Direction Method11.4.3 The Conjugate Gradient Method11.4.4 The C -G Method as an Optimal ProcessChapter 12 Constrained Minimization12.1 Quasi-Newton Methods12.1.1 Modified Newton Method12.1.2 Scaling12.1.3 Memoryless Quasi-Newton Methods12.2 Constrained Minimization Conditions12.2.1 Constraints12.2.2 Tangent Plane12.2.3 First-order Necessary Conditions ( Equality Constraints)12.2.4 Second-order Conditions12.2.5 Eigenvalues in Tangent Subspace12.2.6 Inequality Constraints12.2.7 Zeroth-order Conditions and Lagrange Multipliers12.3 Primal Methods12.3.1 Feasible Direction Methods12.3.2 Active Set Methods12.3.3 The Gradient Projection Method12.3.4 Convergence Rate of the Gradient Projection Method12.3.5 The Reduced Gradient Method12.4 Penalty and Barrier Methods12.4.1 Penalty Methods12.4.2 Barrier Methods12.4.3 Properties of Penalty and Barrier Functions12.5 Dual and Cutting Plane Methods12.5. 1 Global Duality12.5.2 Local Duality12.5.3 Dual Canonical Convergence Rate12.5.4 Separable Problems12.5.5 Decomposition12.5.6 The Dual Viewpoint12.5.7 Cutting Plane Methods12.5.8 Kelley' s Convex Cutting Plane Algorithm12.5.9 Modifications12.6 Primal-dual Methods12.6.1 The Standard Problem12.6.2 Strategies12.6.3 A Simple Merit Function12.6.4 Basic Primal-dual Methods12.6.5 Modified Newton Methods12.6.6 Descent Properties12.6.7 Interior Point Methods Bibliography

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