Non-Interval Uncertainty I: Ellipsoid Uncertainty and its Generalizations
In the previous chapters, we considered the problem of estimating the range of a function f(x1,..., xn) under the assumption that each variable xi, is known to belong to a given interval xi = [x̃i - Δi, x̃i, + Δi]. So far, we have analyzed this problem under the assumption that we do not know of any dependency between the variables xi. Under this assumption, the set of all possible values of \( \vec x \) forms a multi-dimensional interval (box) x1 × ... × xn.
In many practical cases, however, there is a known dependency between the variables xi. For the simplest (quadratic) type of this dependency, the set of all possible values of x⃗ forms an ellipsoid. In this chapter, we analyze the computational complexity and feasibility of data processing under such ellipsoid uncertainty.
KeywordsLinear System Check Consistency Quartic Polynomial Ellipsoid Uncertainty Interval Coefficient
Unable to display preview. Download preview PDF.