Derivatives and Roundoff Errors

Paul Hovland
Seminar

There is a long tradition of using derivatives computed via automatic/algorithmic differentiation (AD) to estimate the impact of roundoff errors in numerical computation (going back at least to Linnainma in 1976). I’ll review some of the AD-based roundoff error estimation methods, describe in more detail the so-called CENA method due to Langlois, and discuss the merits of using forward- versus reverse-mode AD. I’ll finish up with some speculation on other uses for AD in the context of approximate and multi-precision computation.