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Max-linear Systems: Theory and Algorithms / by Peter Butkovič
(Springer Monographs in Mathematics. ISSN:21969922)
版 | 1st ed. 2010. |
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出版者 | (London : Springer London : Imprint: Springer) |
出版年 | 2010 |
本文言語 | 英語 |
大きさ | XVIII, 274 p : online resource |
著者標目 | *Butkovič, Peter author SpringerLink (Online service) |
件 名 | LCSH:Algebras, Linear LCSH:Algebra FREE:Linear Algebra FREE:Algebra |
一般注記 | Max-algebra: Two Special Features -- One-sided Max-linear Systems and Max-algebraic Subspaces -- Eigenvalues and Eigenvectors -- Maxpolynomials. The Characteristic Maxpolynomial -- Linear Independence and Rank. The Simple Image Set -- Two-sided Max-linear Systems -- Reachability of Eigenspaces -- Generalized Eigenproblem -- Max-linear Programs -- Conclusions and Open Problems Recent years have seen a significant rise of interest in max-linear theory and techniques. In addition to providing the linear-algebraic background in the field of tropical mathematics, max-algebra provides mathematical theory and techniques for solving various nonlinear problems arising in areas such as manufacturing, transportation, allocation of resources and information processing technology. It is, therefore, a significant topic spanning both pure and applied mathematical fields. A welcome introduction to the subject of max-plus (tropical) linear algebra, and in particular algorithmic problems, Max-linear Systems: Theory and Algorithms offers a consolidation of both new and existing literature, thus filling a much-needed gap. Providing the fundamentals of max-algebraic theory in a comprehensive and unified form, in addition to more advanced material with an emphasis on feasibility and reachability, this book presents a number of new research results. Topics covered range from max-linear systems and the eigenvalue-eigenvector problem to periodic behavior of matrices, max-linear programs, linear independence, and matrix scaling. This book assumes no prior knowledge of max-algebra and much of the theoryis illustrated with numerical examples, complemented by exercises, and accompanied by both practical and theoretical applications. Open problems are also demonstrated. A fresh and pioneering approach to the topic of Max-linear Systems, this book will hold a wide-ranging readership, and will be useful for: • anyone with basic mathematical knowledge wishing to learn essential max-algebraic ideas and techniques • undergraduate and postgraduate students of mathematics or a related degree • mathematics researchers • mathematicians working in industry, commerce or management HTTP:URL=https://doi.org/10.1007/978-1-84996-299-5 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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Springer eBooks | 9781849962995 |
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EB00234508 |
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