For any poset P , its incidence matrix n and its cover matrix C are the P × P (0, 1) matrices such that n(x, y) = 1 if any only if x is less than y in P and C(x, y) = 1 if any only if x is covered by y in P. It is shown that n and C are conjugate to each other in the incidence algebra of P over a field of characteristic 0 provided P is the nested interval order. In particular, when P is the Bru...

We study bounds on real eigenvalues of interval matrices, and our aim is to develop fast computable formulae that produce as-sharp-as-possible bounds. We consider two cases: general and symmetric interval matrices. We focus on the latter case, since on one hand such interval matrices have many applications in mechanics and engineering, and on the other many results from classical matrix analysi...

The straightforward implementation of interval matrix product suffers from poor efficiency, far from the performances of highly optimized floating-point implementations. In this paper, we show how to reduce the interval matrix multiplication to 9 floating-point matrix products for performance issues without sacrificing the quality of the result. We show that, compared to the straightforward imp...

Two main and not necessarily compatible objectives when implementing the product of two dense matrices with interval coefficients are accuracy and efficiency. In this work, we focus on an implementation on multicore architectures. One direction successfully explored to gain performance in execution time is the representation of intervals by their midpoints and radii rather than the classical re...

Farhadsefat, Rohn and Lotfi defined the concept of an induced interval matrix norm. They then raised the question of finding an interval matrix norm which is not induced by any point matrix norm. We introduce such a norm in this paper.

Results on the inverse interval matrix, both theoretical and computational, are surveyed. Described are, among others, formulae for the inverse interval matrix, NP-hardness of its computation, various classes of interval matrices for which the inverse can be given explicitly, and closed-form formulae for an enclosure of the inverse.