Non-Negative Matrices and Markov Chains

Non-Negative Matrices and Markov Chains pdf epub mobi txt 电子书 下载 2026

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出版者:Springer Verlag 作者:Seneta, E. 出品人: 页数:288 译者: 出版时间:1981-9 价格:$ 145.77 装帧:HRD isbn号码:9780387905983 丛书系列:
图书标签
  • 矩阵理论
  • 马尔可夫链
  • 非负矩阵
  • 概率论
  • 数值分析
  • 随机过程
  • 线性代数
  • 图论
  • 优化
  • 应用数学
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具体描述

This book is a photographic reproduction of the book of the same title published in 1981, for which there has been continuing demand on account of its accessible technical level. Its appearance also helped generate considerable subsequent work on inhomogeneous products of matrices. This printing adds an additional bibliography on coefficients of ergodicity and a list of corrigenda. Eugene Seneta received his Ph.D. in 1968 from the Australian National University. He left Canberra in 1979 to become Professor and Head of the Department of Mathematical Statistics at the University of Sydney. He has been a regular visitor to the United States, most frequently to the University of Virginia. Now Emeritus Professor at the University of Sydney, he has recently developed a renewed interest in financial mathematics. He was elected Fellow of the Australian Academy of Science in 1985 and awarded the Pitman Medal of the Statistical Society of Australia for his distinguished research contributions. The first edition of this book, entitled Non-Negative Matrices, appeared in 1973, and was followed in 1976 by his Regularly Varying Functions in the Springer Lecture Notes in Mathematics, later translated into Russian. Both books were pioneering in their fields. In 1977, Eugene Seneta coauthored (with C. C. Heyde ) I.J. Bienayme : Statistical Theory Anticipated, which is effectively a history of probability and statistics in the 19th century, and in 2001 co-edited with the same colleague Statisticians of the Centuries, both published by Springer. Having served on the editorial board of the Encyclopedia of Statistical Science, he is currently Joint Editor of the International Statistical Review.

这本书聚焦于非负矩阵理论与马尔可夫链之间的紧密联系,深入探讨了这一数学概念在现代应用中的广泛意义。作者以清晰的逻辑结构为读者呈现,首先系统阐述了非负矩阵的基本定义及其在线性代数中的基础地位。通过详细讲解各种典型问题,如图像处理、优化算法以及复杂系统建模等实例,读者能够深刻理解这一理论如何被实际应用于解决复杂问题。在探讨马尔可夫链的角色时,本书进一步揭示了其在概率论和统计分析中的重要地位。作者详细描述了各类状态转移模型的构建方法,并展示了通过计算链的长度、平稳分布以及预测能力等方面的具体技巧。 书中还特别强调非负矩阵理论在解决实际工程问题中的价值,例如在通信信号处理、机器学习算法优化及随机过程建模等领域的应用案例。这些内容不仅帮助读者理解抽象概念,更提供了具体的操作指南,指导他们将理论转化为实际效果。同时,书中对相关数学工具如谱分析、特征值分解和迭代算法的讲解,细致入微地展示了非负矩阵在科学计算中的重要性。这些内容不仅丰富了读者的知识面,还拓宽了他们对现代数据分析技术的认知。 此外,本书注重理论与实践的结合,采用多样化的教学方法和典型案例,使复杂概念变得易于理解。作者通过深入浅出的解释,不仅帮助读者建立坚实的数学基础,还鼓励他们思考如何将这些知识应用到实际问题中。这种讲解风格确保了内容的系统性与完整性,同时保持语言的专业性和可读性。 书中的每一个章节都经过精心设计,旨在为读者提供一个全面的学习框架。作者从基础概念入手,逐步引导读者理解非负矩阵理论的深层内涵,并通过不断强化与实例相结合的方式,让读者真正掌握其应用方法。总体而言,这本书不仅是一本关于数学工具的指南,更是一种思维模式的引导,帮助读者在面对复杂问题时,能够灵活运用所学知识。 整体来看,本书为读者打开了一扇深入探索非负矩阵与马尔可夫链世界的大门,通过严谨的论证和丰富的案例,呈现出这两大主题在科学与工程中的重要地位。它不仅是一本理论的汇编,更是一种学习方法的传递,鼓励读者不断探索、思考,并将所学转化为实际应用。

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