The Overestimation of the Range of a Function in Interval Mathematics with Application to the Solution of Linear Systems of Equations.

摘要

Interval arithmetic was introduced by R. E. Moore in 1966. It helps to get bounds for the range of a function. Sometimes - but not always - these bounds overestimate the range, sometimes they are even extremely pessimistic. In what follows the reasons for this behaviour will be shown. Furthermore criteria are developed which show if a function is 'optimal', i.e. not overestimating the range. An application of this theory to linear systems of equations is given. It produces classes of matrices and of right hand sides for which the Gauss elimination method has this optimality.