Finite Precision Arithmetic

Abstract

Finite precision arithmetic underlies all the computations performed numerically, e.g. in Matlab; only symbolic computations, e.g. Maple, are largely independent of finite precision arithmetic. Historically, when the invention of computers allowed a large number of operations to be performed in very rapid succession, nobody knew what the influence of finite precision arithmetic would be on this many operations: would small rounding errors sum up rapidly and destroy results? Would they statistically cancel? The early days of numerical analysis were therefore dominated by the study of rounding errors, and made this rapidly developing field not very attractive (see the quote above).