The subject of this publication is the minimization of the effects of numerical errors on the performance of digital filters, controllers and adaptive parameter estimators. This minimization is achieved through the use of optimal implementations. The computation of such optimal implementations, which minimise various measures of performance degradation, forms the main part of the book. The novelty is in the wide range of performance criteria, which reflects a range of application areas, and in the computation of the optimal solutions. A typical chapter consists of a problem formulation giving the choice of a performance measure. This is discussed in its relevance and expression in terms of the set of possible realizations, and its minimization.