LOW-COMPLEXITY ZONOTOPES CAN ENHANCE UNCERTAINTY QUANTIFICATION (UQ)

. In many practical situations, the only information that we know about the measurement error is the upper bound Δ on its absolute value. In this case, once we know the measurement result (cid:21) x , the only information that we have about the actual value x of the corresponding quantity is that this value belongs to the interval [ (cid:21) x − Δ , (cid:21) x +Δ] . How can we estimate the accuracy of the result of data processing under this interval uncertainty? In general, computing this accuracy is NP-hard, but in the usual case when measurement errors are relatively small, we can linearize the problem and thus, make computations feasible. This problem is well studied when data processing results in a single value y , but usually, we use the same measurement results to compute the values of several quantities y 1 , . . . , y n . What is the resulting set of tuples ( y 1 , . . . , y n ) ? In this paper, we show that this set is a particular case of what is called a zonotope, and that we can use known results about zonotopes to make the corresponding computational problems easier to solve.