منابع مشابه
Max-Plus Convex Geometry
Max-plus analogues of linear spaces, convex sets, and polyhedra have appeared in several works. We survey their main geometrical properties, including max-plus versions of the separation theorem, existence of linear and non-linear projectors, max-plus analogues of the Minkowski-Weyl theorem, and the characterization of the analogues of “simplicial” cones in terms of distributive lattices.
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-Plus Quasi-interpretations
Résumé Quasi-interpretations are a tool to bound the size of the values computed by a first-order functional program (or a term rewriting system) and thus a mean to extract bounds on its computational complexity. We study the synthesis of quasi-interpretations selected in the space of polynomials over the max-plus algebra determined by the non-negative rationals extended with −∞ and equipped wi...
متن کاملMax-plus LU
We present a new method for the a priori approximation of the order of magnitude of the entries in the LU factors of a matrix A ∈ Cn×n. We are also able to predict which permutation matrices will be chosen by partial pivoting or complete pivoting Gaussian elimination. Our method uses maxplus algebra and is based purely on the modulii of the entries in the matrix. This approximation can be used ...
متن کاملMax-plus Singular Values
In this paper we prove a new characterization of the max-plus singular values of a maxplus matrix, as the max-plus eigenvalues of an associated max-plus matrix pencil. This new characterization allows us to compute max-plus singular values quickly and accurately. As well as capturing the asymptotic behavior of the singular values of classical matrices whose entries are exponentially parameteriz...
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ژورنال
عنوان ژورنال: Jurnal Ilmiah Matematika dan Pendidikan Matematika
سال: 2012
ISSN: 2550-0422,2085-1456
DOI: 10.20884/1.jmp.2012.4.2.2965