The paper presents interval-affine Gaussian algorithm for the interval linear systemsAx = b subject to some constraints on real matrices A from the interval matrix A. The interval-affine method is based on the so-called interval-affine arithmetic that allows to take the constraints into account during the computation of interval enclosures of the united solution set of the system Ax = b, and to...

This paper provides a simple proof for the Perron-Frobenius theorem concerned with positive matrices using a homotopy technique. By analyzing the behaviour of the eigenvalues of a family of positive matrices, we observe that the conclusions of Perron-Frobenius theorem will hold if it holds for the starting matrix of this family. Based on our observations, we develop a simple numerical technique...

A method for enclosing matrix polynomials is proposed. This method is applicable when the matrix is diagonalizable and supplies an interval matrix including the matrix polynomial. The computational cost of this method does not depend on the degree of the polynomial. Hence the proposed method is faster than previous approaches when the degree is large. Numerical results show the properties of th...

We propose an eigenvalue contractor for symmetric matrices. Given a symmetric interval matrix A and an interval approximation of its eigenvalue sets λ1, . . . ,λn the contractor reduces the entries of A S such that no matrix with eigenvalues in λ1, . . . ,λn is omitted. Our contractor is based on sequentially reducing the entries of A. We discuss properties of the method and demonstrate its per...

It is proved that applying sufficient regularity conditions to the interval matrix [A − |B|, A + |B|], we can create a new unique solvability condition for the absolute value equation Ax + B|x| = b, since regularity of interval matrices implies unique solvability of their corresponding absolute value equation. This condition is formulated in terms of positive definiteness of a certain point mat...

The numerical computation of the exponentiation of a real matrix has been intensively studied. The main objective of a good numerical method is to deal with round-off errors and computational cost. The situation is more complicated when dealing with interval matrices exponentiation: Indeed, the main problem will now be the dependency loss of the different occurrences of the variables due to int...

Stability analysis of linear circuits and systems under interval parameter uncertainties can be equated to estimating the eigenvalues of interval matrices. In this paper, the problem of determining outer bounds on the ranges of the real eigenvalues is considered. A method for computing such bounds is suggested. It consist of setting up and solving a system of n nonlinear equations, n being the ...

Consider linear algebraic systems where the elements of the matrix and the right-hand side vector depend linearly on a number of interval parameters. We prove some sufficient conditions for the united parametric solution set of such a system to have linear boundary. These conditions imply an equivalent representation of the parametric system where each parameter appears once in a diagonal matri...

A binary matrix M has the Consecutive Ones Property (COP) if there exists a permutation of columns that arranges the ones consecutively in all the rows. Given a matrix, the d-COS-R problem is to determine if there exists a set of at most d rows whose deletion results in a matrix with COP. We consider the parameterized complexity of this problem with respect to the number d of rows to be deleted...