Title page for ETD etd-05042009-152934


Type of Document Master's Thesis
Author Farlow, Kasie Geralyn
Author's Email Address kfar1228@vt.edu
URN etd-05042009-152934
Title Max-Plus Algebra
Degree Master of Science
Department Mathematics
Advisory Committee
Advisor Name Title
Day, Martin V. Committee Chair
Haskell, Peter E. Committee Member
Wheeler, Robert L. Committee Member
Keywords
  • Markov Chains
  • Linear Algebra
  • Max-Plus
Date of Defense 2009-04-27
Availability unrestricted
Abstract
In max-plus algebra we work with the max-plus semi-ring which is the set Rmax=[-infinity,infinity) together with operations "a+b"=max(a,b) and "ab"= a +b.  The additive and multiplicative identities are taken to be

epsilon=-infinity and e=0 respectively. Max-plus algebra is one of many idempotent semi-rings which have been considered in various
fields

of mathematics. Max-plus algebra is becoming more popular not only because its operations are associative, commutative and distributive as

in conventional algebra but because it takes systems that are non-linear in conventional algebra and makes them linear.  Max-plus

algebra also arises as the algebra of asymptotic growth rates of functions in conventional algebra which will play a significant role in several aspects of this thesis. This thesis is a survey of max-plus algebra that will concentrate on max-plus linear
algebra results. We will then consider from a max-plus perspective several results by Wentzell and Freidlin for finite state Markov chains with an asymptotic dependence.

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