Lie groups and error analysis (Q2718668)

The authors outline a new approach to error analysis in floating point arithmetics. It is based on the observation that many numerical procedures can be viewed as the computation of a group product. The authors develop the general theory of some invariant metrics on Lie groups and on the associated homogeneous spaces needed to error estimates. Constructing these metrics they obtain explicit error estimates for a floating point implementation of Horner's algorithm and compare these estimates with observed errors. The paper is complemented by K. H. Hofmann's appendix on the existence of the invariant metrics in question on more general groups. This enlarges the perspectives of application of the presented method for error analysis.