Round-off errors coming from numerical calculation finite precision can lead to catastrophic losses in significant numbers when they accumulate. Existing analytical error bounds are known to be poorly scalable become unusable for large problems. That is why the propagation of round-off errors throughout a computation needs to be better understood in order to ensure large-scale application result accuracy. We will present a round-off error estimation method based on a running error analysis and implemented similarly to automatic differentiation techniques. It can help following the error propagation through a computational graph and identifying the main sources of error affecting the final results. It has been experimented on LU decomposition algorithms that are widely used to solve linear systems. We will provide some examples as well as new challenges that need to be tackled in the future in order to analyze round-off error propagation in large-scale problems.

Bio:
Vincent Baudoui is a postdoctoral fellow at Argonne funded by Total SA. He received his PhD from ISAE Toulouse, France in 2012 in the field of optimization under uncertainty. His current research topics involve round-off error propagation in large scale numerical simulations as well as non-deterministic behaviors in parallel systems.