On Guaranteed Accuracy Computation

The concept of guaranteed accuracy computation is a natural one: the user could specify any á priori relative or absolute precision bound on the numerical values which are to be computed in an algorithm. It is a generalization of guaranteed sign computation, a concept originally proposed to solve the ubiquitous problem of non-robustness in geometric algorithms. In this paper, we investigate some basic properties of such computational mode. We formulate a theory of real computation and approximation to capture guaranteed accuracy computation. We also introduce an algebraic and a numerical model of computation based on Schönhage’s pointer machines.