Infimum-supremum interval arithmetic is widely used because of ease of implementation and narrow results. In this note we show that the overestimation of midpoint-radius interval arithmetic compared to power set operations is uniformly bounded by a factor 1.5 in radius. This is true for the four basic operations as well as for vector and matrix operations, over real and over complex numbers. Mo...

Suppose that we have one run of n observations of a stochastic process by means of computer simulation and would like to construct a condifence interval for the steady-state mean of the process. Seeking for independent observations, so that the classical statistical methods could be applied, we can divide the n observations into k batches of length m (n= k.m) or alternatively, transform the cor...

An interval vector is a (0, 1)-vector in Rn for which all the 1’s appear consecutively, and an interval-vector polytope is the convex hull of a set of interval vectors in Rn. We study three particular classes of interval vector polytopes which exhibit interesting geometric-combinatorial structures; e.g., one class has volumes equal to the Catalan numbers, whereas another class has face numbers ...

Vector Fitting is an effective technique for rational approximation of LTI systems. It has been extended to fit the magnitude of the transfer function in absence of phase data. In this paper, magnitude Vector Fitting is modified to work on inequalities which the magnitude of the transfer function has to satisfy, instead of least squares approximation. The new interval version of the magnitude V...

Imprecision, incompleteness, prior knowledge or improved learning speed can motivate interval–represented data. Most approaches for SVM learning of interval data use local kernels based on interval distances. We present here a novel approach, suitable for linear SVMs, which allows to deal with interval data without resorting to interval distances. The experimental results confirms the validity ...