Dewey Class |
512.5 |
Title |
Max-linear Systems: Theory and Algorithms ([Ebook]) / 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 |
Links to Related Works |
Subject References:
Authors:
Corporate Authors:
Series:
Classification:
|