Structural Analysis on Interval Matrices by Signed Digraph: Determinant Maximization and Singularity
نویسنده
چکیده
We present some results that show the information of sign structure of matrices characterized by signed digraph can reduce computations in interval matrices. With the sign structure of the matrices, vertices of interval matrices which realizes the max/min of the determinant can be xed. We present an algorithm to check singularity of interval matrices based on the result. We also discuss impact of this approach to other problems of interval systems.
منابع مشابه
Structural Analysis on Interval Matrices by Signed Digraph: Structural Perturbation Principle
This note deals with linear interval systems whose parameters in system matrix are expressed by intervals. We formalize the system reasoning about structures of interval systems by the structural perturbation principle: the interval system would have the interval property when its underlying sign structure include the component that has the corresponding sign property and the norm of the rest o...
متن کاملRepresenting digraphs using intervals or circular arcs
Containment and overlap representations of digraphs are studied, with the following results. The interval containment digraphs are the digraphs of Ferrers dimension 2, and the circular-arc containment digraphs are the complements of circular-arc intersection digraphs. A poset is an interval containment poset if and only if its comparability digraph is an interval containment digraph, and a grap...
متن کاملTwin signed total Roman domatic numbers in digraphs
Let $D$ be a finite simple digraph with vertex set $V(D)$ and arcset $A(D)$. A twin signed total Roman dominating function (TSTRDF) on thedigraph $D$ is a function $f:V(D)rightarrow{-1,1,2}$ satisfyingthe conditions that (i) $sum_{xin N^-(v)}f(x)ge 1$ and$sum_{xin N^+(v)}f(x)ge 1$ for each $vin V(D)$, where $N^-(v)$(resp. $N^+(v)$) consists of all in-neighbors (resp.out-neighbors) of $v$, and (...
متن کاملSufficient Conditions for Regularity and Singularity of Interval Matrices
Several verifiable sufficient conditions for regularity and singularity of interval matrices are given. As an application, a verifiable sufficient condition is derived for an interval matrix to have all eigenvalues real.
متن کاملAn 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 کامل