Improving Interval Analysis Bounds by Translations

Improving Interval Analysis

Improving probability bounds by optimization over subsets

The simple device of maximization over subsets of events can provide substantial improvement over the Dawson–Sankoff degree two lower bound on the probability of a union of events and can also exceed a sharper bound that uses individual and pairwise joint event probabilities developed by Kuai, Alajaji, and Takahara. In each of their examples, the maximized bound achieves the exact probability o...

Analysis of Eigenvalue Bounds for Real Symmetric Interval Matrices

In this paper, we present several verifiable conditions for eigenvalue intervals of real symmetric interval matrices overlapping or not overlapping. To above cases, two new methods with algorithms for computing eigenvalue bounds of real symmetric matrices are developed. We can estimate eigenvalue bounds moving away the assumption that two intervals containing two eigenvalues of real symmetric i...

Interval Kalman filter enhanced by positive definite upper bounds

A method based on the interval Kalman filter for discrete uncertain linear systems is presented. The system under consideration is subject to bounded parameter uncertainties not only in the state and observation matrices, but also in the covariance matrices of Gaussian noises. The gain matrix provided by the filter is optimized to give a minimal upper bound on the state estimation error covaria...

Improving interval enclosures

This paper serves as background information for the Vienna proposal for interval standardization, explaining what is needed in practice to make competent use of the interval arithmetic provided by an implementation of the standard to be. Discussed are methods to improve the quality of interval enclosures of the range of a function over a box, considerations of possible hardware support facilita...