Topic status: We're looking for students to study this topic.
An important problem in numerical linear algebra is the accurate and efficient computation of a matrix exponential, or related function. Such a need arises, for example, in the solution of linear ODEs. Published in 1978, the famous paper after which this project is named described 19 different ways in which this might be achieved. These days, there is an ever-growing transition towards parallel computing, and many of these methods are no longer considered applicable. Instead, a need arises to search for new methods that might be more amenable to parallelisation; or at least to re-evaluate old methods within this new context. This project would involve an investigation into the applicability of some of these methods. Depending on the student's programming background, this could involve implementing these schemes in MATLAB on a desktop PC, through to implementing them in C++ on a hybrid CPU/GPU machine.