Max-linear Systems: Theory and Algorithms

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 su...

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主要作者: Butkovič, Peter
格式: Livre numérique
語言:Anglais
出版: London : Springer London [20..].
Cham : Springer Nature
版:1st ed. 2010.
叢編:Springer Monographs in Mathematics
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Edition sous un autre format:• Max-linear systems, theory and algorithms, Peter Butkovič, London, Springer, 2010, 1 vol. (XVII-272 p.), Springer monographs in mathematics, 978-1-84996-298-8
• Max-linear systems, theory and algorithms, Peter Butkovič, London, Springer, 2010, 1 vol. (XVII-272 p.), Springer monographs in mathematics, 978-1-84996-298-8
• Max-linear Systems: Theory and Algorithms, Texte imprimé, 9781447125839
• Max-linear Systems: Theory and Algorithms, Texte imprimé, 9781849963008
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505 1 |a 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 
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520 |a 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 
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