Max-Plus Algebra
| dc.contributor.author | Farlow, Kasie Geralyn | en |
| dc.contributor.committeechair | Day, Martin V. | en |
| dc.contributor.committeemember | Haskell, Peter E. | en |
| dc.contributor.committeemember | Wheeler, Robert L. | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessioned | 2014-03-14T20:35:01Z | en |
| dc.date.adate | 2009-05-26 | en |
| dc.date.available | 2014-03-14T20:35:01Z | en |
| dc.date.issued | 2009-04-27 | en |
| dc.date.rdate | 2009-05-26 | en |
| dc.date.sdate | 2009-05-04 | en |
| dc.description.abstract | In max-plus algebra we work with the max-plus semi-ring which is the set ℝ<sub>max</sub>=[-∞)∪ℝ together with operations 𝑎⊕𝑏 = max(𝑎,𝑏) and 𝑎⊗𝑏= 𝑎+𝑏. The additive and multiplicative identities are taken to be ε=-∞ and ε=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. | en |
| dc.description.degree | Master of Science | en |
| dc.identifier.other | etd-05042009-152934 | en |
| dc.identifier.sourceurl | http://scholar.lib.vt.edu/theses/available/etd-05042009-152934/ | en |
| dc.identifier.uri | http://hdl.handle.net/10919/32191 | en |
| dc.publisher | Virginia Tech | en |
| dc.relation.haspart | Finalthesis.pdf | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject | Markov Chains | en |
| dc.subject | Linear Algebra | en |
| dc.subject | Max-Plus | en |
| dc.title | Max-Plus Algebra | en |
| dc.type | Thesis | en |
| thesis.degree.discipline | Mathematics | en |
| thesis.degree.grantor | Virginia Polytechnic Institute and State University | en |
| thesis.degree.level | masters | en |
| thesis.degree.name | Master of Science | en |
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