We have investigated the use of computer algebra as the basis for software tools for floating-point error analysis in Maple. We looked at the properties of the error-propagation factors of the differential error model to fully understand the circumstances under which the factors become large. In addition, we look at the measures that must be taken to assure that a reformulation improves the stability of a computation and formulate a basic principle of reformulation.We are able to show that a breadth-first traversal of the computational graph is a practical and efficient strategy to employ when performing an error analysis based on the differential error model. We show that the strategy can reduce the number of propagation factors that need to be studied and can identify the component of the computation that requires modification to improve stability. Not all propagation factors need to be considered.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.