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Functions of matrices underpin many of the fundamental algorithms used in the finance, engineering and pharmaceutical industries. Our research has provided the state of the art algorithms for computing the most common matrix functions. The algorithms have been implemented commercially in MATLAB (with almost 2 million users) and the Numerical Algorithms Group (NAG) Ltd Library; as well as in open source packages such as R and Eigen. Software companies have enjoyed direct impact through improved products and increased revenues, whilst the greater indirect impact is for the users of the software, leading to acceleration in the pace of science and engineering worldwide.
In the late 1990s, a significant barrier to the adoption of virtual reality software was the expense of manually creating models of real-world scenes. To address this, between 1998 and 2004, the ICARUS software system was developed, which enabled the creation of structured, 3D geometric models from a sequence of images or video. The system also pioneered improved methods of camera tracking. ICARUS was subsequently licensed and developed commercially, and became the foundation for video and film post-production products that are used worldwide in the film (e.g. Universal Pictures, Warner Bros, Paramount Pictures) and television (e.g. BBC) industries, underpinning a company with an annual turnover in excess of £1m.