Review on stochastic approach to round-off error analysis and its applications (Q1116286)

A mathematical expression f(x) is considered which is to be evaluated on a computer. It is assumed that f(x) consists of a series of arithmetical operations as well as of functions, where the data x is to be processed. The permutation method consists in a fictitious application of all computer codes \(p_ i(x)\) to the data x which are syntactically equivalent to f(x). Let us pick out one of the codes, \(p_ i(x)\). Then the perturbation method consists in collecting all those possible results which are gained by executing the code \(p_ i(x)\), where, at each individual step of the execution, rounding upwards as well as rounding downwards is used. The permutation-perturbation method consists now in applying the perturbation principle to each code \(p_ i(x)\). The set of all these numerical values is starting point for a thorough error analysis of computationally evaluating f(x). - The paper presents the state of the art of the method as well as of its numerous applications.