Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). Almost every key calculation supporting science and engineering depends implicitly or explicitly on the work of numerical analysts.
The Numerical Analysis Group is a research-led team of mathematicians that provides core expertise in this area to STFC and the wider UK community. Our specialities include sparse linear algebra (the solution of millions of simultaneous equations where most of the coefficients are zero) and optimization (finding the best answer perhaps subject to constraints).
As computer technology evolves, effective algorithms must be designed, analysed and implemented to take full advantage of new capabilities whilst maintaining mathematical guarantees on their accuracy. By expanding the size of problems that can be solved, not only can scientists and engineers be more productive, but it becomes possible to tackle areas that were previously infeasible.
Our research involves mathematical problems as well as those arising from technological challenges, such as finding parallelism in traditionally serial algorithms. We have been pivotal in the development of new techniques such as multi-frontal factorization, profile reduction, cubic overestimation and nonlinear programming funnels, and continue to expand the range of problems that can be satisfactorily solved through optimization and other areas that depend on sparse linear algebra.
The Group's ongoing research feeds into two state-of-the-art mathematical software libraries, HSL and GALAHAD that are used across a diverse range of areas from plasma modelling through material design, entertainment, finance and robotics.