A linear, robust and convergent interpolatory algorithm for quantifying model uncertainties

The authors present a linear, interpolatory, convergent uncertainty estimation scheme which is robust in the face of disturbance. The idea is that by simply changing from Lagrange interpolation to Hermite interpolation an effective scheme is derived for estimation of uncertainty. It is shown that the proposed scheme has the advantage that in the face of corrupted data, the error in the derived uncertainty bound is independent of the degree of the approximating polynomial, i.e., if ∈ denotes the maximum magnitude of the disturbance, then the maximum possible error in the uncertainty bound is ⩽∈