Complexity Analysis of Automatic Differentiation in the Hyperion Software

Abstract

One important feature of the hyperion software is the rational approximation problem: given the m first terms of the power series expansion of a stable transfer function, find a stable approximation of it under the form P/q, of McMillan degree n. This leads to minimising ψ(Q), for some Q. In this chapter, we show different ways of computing ψ and its derivatives, and we indicate the complexity of these computations.