From Rounding Error Estimation to Automatic Correction with Automatic Differentiation
Résumé
Using automatic differentiation (AD) to estimate the propagation of rounding errors in numerical algorithms is classic. We propose a new application of AD to roundoff analysis providing an automatic correction of the first order effect of the elementary rounding errors. We present the main characteri- stics of this method and significant examples of its application to improve the accuracy of computed results and/or the stability of the algorithm.