An Algorithm for Checking Regularity of Interval Matrices
نویسندگان
چکیده
منابع مشابه
An Algorithm for Checking Regularity of Interval Matrices
Checking regularity (or singularity) of interval matrices is a known NP-hard problem. In this paper a general algorithm for checking regularity/singularity is presented which is not a priori exponential. The algorithm is based on a theoretical result according to which regularity may be judged from any single component of the solution set of an associated system of linear interval equations. Nu...
متن کاملA Note on Checking Regularity of Interval Matrices
It is proved that two previously known sufficient conditions for regularity of interval matrices are equivalent in the sense that they cover the same class of interval matrices.
متن کاملAn Optimal Algorithm for Checking Regularity
We present a deterministic algorithm A that, in O(m2) time, verifies whether a given m by m bipartite graph G is regular, in the sense of Szemerédi [E. Szemerédi, Regular partitions of graphs, Problèmes Combinatoires et Théorie des Graphes (Colloq. Internat. CNRS, Univ. Orsay, Orsay, 1976) (Paris), Colloques Internationaux CNRS n. 260, 1978, pp. 399–401]. In the case in which G is not regular e...
متن کاملAE regularity of interval matrices
Consider a linear system of equations with interval coefficients, and each interval coefficient is associated with either a universal or an existential quantifier. The AE solution set and AE solvability of the system is defined by $\forall\exists$-quantification. Herein, we deal with the problem what properties must the coefficient matrix have in order that there is guaranteed an existence of a...
متن کاملAn Algorithm for Checking Strong Regularity of Matrices in Bottleneck Algebras
Let (B, ≤) be a dense, linearly ordered set without maximum and minimum and (⊕, ⊗) = (max, min). An n × n matrix A = (a ij) over B is called (a) strongly regular if for some b the system A ⊗ x = b is uniquely solvable; (b) trapezoidal if the inequality a ii > i k=1 n l=k+1 a kl holds for all i = 1, .., n. We show that a square matrix is strongly regular if and only if it can be transformed to a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 1999
ISSN: 0895-4798,1095-7162
DOI: 10.1137/s0895479896313978