Algorithmic Differentiation with Intervals

The computational solution of many mathematical problems involves derivatives. Furthermore, in search of verified computer results, it is necessary to construct algorithms for interval inclusions of derivatives. For “small” functions hand-coded formulas for derivatives and appropriate algorithms for interval inclusions are possible, but for “large” functions algorithmic methods have to be employed. In this lecture we screen the complexity of algorithmic differentiation methods, and we investigate the quality of corresponding interval inclusions of derivatives.