منابع مشابه
Matrix period in max-drast fuzzy algebra
Periods of matrix power sequences in max-drast fuzzy algebra and methods of their computation are considered. Matrix power sequences occur in the theory of complex fuzzy systems with transition matrix in max-t algebra, where t is a given triangular fuzzy norm. Interpretation of a complex system in max-drast algebra reflects the situation when extreme demands are put on the reliability of the sy...
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...
متن کاملCsr Expansions of Matrix Powers in Max Algebra
We study the behavior of max-algebraic powers of a reducible nonnegative matrix A ∈ Rn×n + . We show that for t ≥ 3n2, the powers At can be expanded in max-algebraic sums of terms of the form CStR, where C and R are extracted from columns and rows of certain Kleene stars, and S is diagonally similar to a Boolean matrix. We study the properties of individual terms and show that all terms, for a ...
متن کاملMatrix factorization over max-times algebra for data mining
Decomposing a given matrix into two factor matrices is a frequently used technique in data mining for uncovering underlying latent patterns in the data. Unlike in pure mathematics, the emphasis is put on obtaining results that are interpretable, rather than necessarily having a small reconstruction error. One approach to increase interpretability is to pose constraints on the factors. For examp...
متن کاملLinear 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...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2000
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(99)00242-5