A note on the perturbation of arithmetic expressions

Abstract EN

In this paper we present the theoretical foundation of forward error analysis of numerical algorithms under;  Approximations in "built-in" functions.

 Rounding errors in arithmetic floating-point operations.

 Perturbations of data.

The error analysis is based on linearization method.

The fundamental tools of the forward error analysis are system of linear absolute and relative a prior and a posteriori error equations and associated condition numbers constituting optimal of possible cumulative round – off errors.

The condition numbers enable simple general, quantitative bounds definitions of numerical stability.

The theoretical results have been applied a Gaussian elimination, and have proved to be very effective means of both a priori and a posteriori error analysis.