Estimating computational noise.

Abstract

Computational noise in deterministic simulations is as ill-defined a concept as can be found in scientific computing. When coupled with adaptive strategies, the effects of finite precision destroy smoothness of the simulation output and complicate subsequent analysis. Following the work of Hamming on roundoff errors, we present a new algorithm, ECnoise, for quantifying the noise level of a computed function. Our theoretical framework is based on stochastic noise but does not assume a specific distribution for the noise. For the deterministic simulations considered, ECnoise produces reliable results in a few function evaluations and offers new insights into building blocks of large scale simulations.