Round-off Error Propagation Using Derivatives
Round-off errors coming from numerical calculation finite precision can lead to catastrophic losses in significant numbers when they accumulate. Their propagation throughout a computation needs to be studied in order to ensure results accuracy. We present a round-off error estimation method based on first order derivatives computed thanks to algorithmic differentiation techniques. It can help following error propagation in an execution graph and identifying the sensitive sections of a code. It has been experimented on well known LU decomposition algorithms. We will present some examples as well as challenges that need to be tackled as part of future research work in order to set up a strategy to analyze round-off error propagation in large scale problems.
Vincent Baudoui is a postdoctoral fellow at Argonne funded by Total SA, a major French oil and gas company. 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.