Max-linear Systems: Theory and Algorithms

  • Peter Butkovič

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Peter Butkovič
    Pages 1-39
  3. Peter Butkovič
    Pages 41-52
  4. Peter Butkovič
    Pages 71-101
  5. Peter Butkovič
    Pages 103-126
  6. Peter Butkovič
    Pages 149-178
  7. Peter Butkovič
    Pages 179-225
  8. Peter Butkovič
    Pages 227-241
  9. Peter Butkovič
    Pages 243-257
  10. Peter Butkovič
    Pages 259-260
  11. Back Matter
    Pages 261-272

About this book

Introduction

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

Keywords

Characteristic Polynomial Eigenvalue Eigenvalues and Eigenvectors Eigenvector Linear Independence Linear System Matrix Orbit Matrix Scaling Max-algebra

Authors and affiliations

  • Peter Butkovič
    • 1
  1. 1., School of MathematicsUniversity of BirminghamBirminghamUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-84996-299-5
  • Copyright Information Springer-Verlag London Limited 2010
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-84996-298-8
  • Online ISBN 978-1-84996-299-5
  • Series Print ISSN 1439-7382
  • About this book