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Max-linear Systems: Theory and Algorithms

Max-linear Systems: Theory and Algorithms
Catalogue Information
Field name Details
Dewey Class 512.5
Title Max-linear Systems: Theory and Algorithms (EB) / by Peter Butkovič
Author Butkovič, Peter
Other name(s) SpringerLink (Online service)
Publication London : Springer London
, 2010.
Physical Details XVIII, 274 pages : online resource.
Series Springer monographs in mathematics 1439-7382
ISBN 9781849962995
Summary Note 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:
Contents note Introduction -- 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.
System details note Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site http://dx.doi.org/10.1007/978-1-84996-299-5
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