Linear systems in (max, +) algebra

Marianne Akian; Guy Cohen; Stephane Gaubert; Ramine Nikoukhah; Jean Pierre Quadrat

Linear systems in (max, +) algebra

Marianne Akian
, Guy Cohen
, Stephane Gaubert
, Ramine Nikoukhah
, Jean Pierre Quadrat

INRIA Institut National de Recherche en Informatique et en Automatique

Research output: Contribution to journal › Conference article › peer-review

28 Citations (Scopus)

Abstract

The general system of linear equations in the (max, +) algebra is studied. A symmetrization of this algebra and a new notion called balance which generalizes classical equations are introduced. This construction results in the linear closure of the (max, +) algebra in the sense that every non-degenerate system of linear balances has a unique solution given by Cramer's rule.

Original language	English
Pages (from-to)	151-156
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	1
Publication status	Published - 1 Dec 1990
Event	Proceedings of the 29th IEEE Conference on Decision and Control Part 6 (of 6) - Honolulu, HI, USA Duration: 5 Dec 1990 → 7 Dec 1990

Cite this

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title = "Linear systems in (max, +) algebra",

abstract = "The general system of linear equations in the (max, +) algebra is studied. A symmetrization of this algebra and a new notion called balance which generalizes classical equations are introduced. This construction results in the linear closure of the (max, +) algebra in the sense that every non-degenerate system of linear balances has a unique solution given by Cramer's rule.",

author = "Marianne Akian and Guy Cohen and Stephane Gaubert and Ramine Nikoukhah and Quadrat, \{Jean Pierre\}",

year = "1990",

month = dec,

day = "1",

language = "English",

volume = "1",

pages = "151--156",

journal = "Proceedings of the IEEE Conference on Decision and Control",

issn = "0743-1546",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

note = "Proceedings of the 29th IEEE Conference on Decision and Control Part 6 (of 6) ; Conference date: 05-12-1990 Through 07-12-1990",

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TY - JOUR

T1 - Linear systems in (max, +) algebra

AU - Akian, Marianne

AU - Cohen, Guy

AU - Gaubert, Stephane

AU - Nikoukhah, Ramine

AU - Quadrat, Jean Pierre

PY - 1990/12/1

Y1 - 1990/12/1

N2 - The general system of linear equations in the (max, +) algebra is studied. A symmetrization of this algebra and a new notion called balance which generalizes classical equations are introduced. This construction results in the linear closure of the (max, +) algebra in the sense that every non-degenerate system of linear balances has a unique solution given by Cramer's rule.

AB - The general system of linear equations in the (max, +) algebra is studied. A symmetrization of this algebra and a new notion called balance which generalizes classical equations are introduced. This construction results in the linear closure of the (max, +) algebra in the sense that every non-degenerate system of linear balances has a unique solution given by Cramer's rule.

M3 - Conference article

AN - SCOPUS:0025567902

SN - 0743-1546

VL - 1

SP - 151

EP - 156

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

T2 - Proceedings of the 29th IEEE Conference on Decision and Control Part 6 (of 6)

Y2 - 5 December 1990 through 7 December 1990

ER -

Linear systems in (max, +) algebra

Abstract

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