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 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

Contenu
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.