Idempotent/tropical analysis, the Hamilton-Jacobi and Bellman equations

Autor:	Litvinov, Grigory L.
Rok vydání:	2012
Předmět:	Mathematics - Rings and Algebras Mathematical Physics Mathematics - Functional Analysis Mathematics - Numerical Analysis 15A80 35F21 65F05 65F99 65G40 46E05 46T99 52B12
Druh dokumentu:	Working Paper
Popis:	Tropical and idempotent analysis with their relations to the Hamilton-Jacobi and matrix Bellman equations are discussed. Some dequantization procedures are important in tropical and idempotent mathematics. In particular, the Hamilton-Jacobi-Bellman equation is treated as a result of the Maslov dequantization applied to the Schr\"{o}dinger equation. This leads to a linearity of the Hamilton-Jacobi-Bellman equation over tropical algebras. The correspondence principle and the superposition principle of idempotent mathematics are formulated and examined. The matrix Bellman equation and its applications to optimization problems on graphs are discussed. Universal algorithms for numerical algorithms in idempotent mathematics are investigated. In particular, an idempotent version of interval analysis is briefly discussed. Comment: 70 pages, 5 figures, CIME lectures (2011), to be published in Lecture Notes in Mathematics (Springer)
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1203.0522 Zobrazit plný text záznamu View this record from Arxiv