منابع مشابه
Linear systems in (max,+) algebra
Proceedings of the 29th Conference on Decision and Control Honolulu, Dec. 1990 Abstract In this paper, we study the general system of linear equations in the algebra. We introduce a symmetrization of this algebra and a new notion called balance which generalizes classical equations. This construction results in the linear closure of the algebra in the sense that every nondegenerate system of li...
متن کاملMax-plus algebra
The max-plus semiring Rmax is the set R∪{−∞}, equipped with the addition (a, b) 7→ max(a, b) and the multiplication (a, b) 7→ a + b. The identity element for the addition, zero, is −∞, and the identity element for the multiplication, unit, is 0. To illuminate the linear algebraic nature of the results, the generic notations +, , × (or concatenation), 0 and 1 are used for the addition, the sum, ...
متن کاملMax-algebra: the linear algebra of combinatorics?
Let a ⊕ b = max(a, b), a ⊗ b = a + b for a, b ∈ R := R ∪ {−∞}. By max-algebra we understand the analogue of linear algebra developed for the pair of operations (⊕,⊗) extended to matrices and vectors. Max-algebra, which has been studied for more than 40 years, is an attractive way of describing a class of nonlinear problems appearing for instance in machinescheduling, information technology and ...
متن کاملTimetable Synthesis Using (max,+) Algebra
This paper deals with control of transportation systems. We propose an approach based on dioid theory to compute timetables of a transportation network. We generalize the problem by considering additional constraints for the control objective. Copyright c ©2006 IFAC
متن کاملOn matrix powers in max-algebra
Let A = (aij ) ∈ Rn×n,N = {1, . . . , n} and DA be the digraph (N, {(i, j); aij > −∞}). The matrix A is called irreducible if DA is strongly connected, and strongly irreducible if every maxalgebraic power of A is irreducible. A is called robust if for every x with at least one finite component, A(k) ⊗ x is an eigenvector of A for some natural number k. We study the eigenvalue–eigenvector proble...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2004
ISSN: 0024-3795
DOI: 10.1016/j.laa.2004.03.022