Max-linear Systems: Theory and Algorithms

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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

Author(s): Peter Butkovič (auth.)
Series: Springer Monographs in Mathematics
Edition: 1
Publisher: Springer-Verlag London
Year: 2010

Language: English
Pages: 274
Tags: Linear and Multilinear Algebras, Matrix Theory

Front Matter....Pages I-XVII
Introduction....Pages 1-39
Max-algebra: Two Special Features....Pages 41-52
One-sided Max-linear Systems and Max-algebraic Subspaces....Pages 53-70
Eigenvalues and Eigenvectors....Pages 71-101
Maxpolynomials. The Characteristic Maxpolynomial....Pages 103-126
Linear Independence and Rank. The Simple Image Set....Pages 127-148
Two-sided Max-linear Systems....Pages 149-178
Reachability of Eigenspaces....Pages 179-225
Generalized Eigenproblem....Pages 227-241
Max-linear Programs....Pages 243-257
Conclusions and Open Problems....Pages 259-260
Back Matter....Pages 261-272