Before revision:  We provide an algorithm that does not need such an exhaustive search, and show that the best possible bounds for the amplitude can be obtained propagating complex pairs only from the convex hull  . Because the convex hull is always tightly inscribed in the respective rigorous bounding box resulting from interval arithmetic, we conclude that the obtained bounds are guaranteed to yield the true bounds .
After revision:  We provide an algorithm that does not need such an exhaustive search, and show that the best possible bounds for the amplitude can be obtained propagating complex pairs only from the convex hull of endpoints at each term of the Fourier series . Because the convex hull is always tightly inscribed in the respective rigorous bounding box resulting from interval arithmetic, we conclude that the obtained bounds are guaranteed to yield the true bounds .