MATFUN · Functions of Matrices: Theory and Computation

Functions of matrices are widely used in science, engineering and the social sciences, due to the succinct and insightful way they allow problems to be formulated and solutions to be expressed. New applications involving matrix functions are regularly being found, ranging from small but difficult problems in medicine to huge, sparse systems arising in the solution of partial differential equations. The objective of this research is to make breakthroughs in theory and algorithms that will have a major impact on applications that employ matrix functions. Productive lines of enquiry and novel methodological approaches have been identified across the spectrum of the subject. In the theory, significant advances on nonprimary functions, structured matrices, and nonnormality will be obtained. New and improved algorithms for evaluating of a variety of functions as well as their Fréchet derivatives and condition numbers will be developed. For the key problem of computing the action of a matrix function on a vector a highly promising, novel approach for the matrix exponential will be developed and applied within exponential integrators. Massively parallel machines will be targeted by developing asynchronous algorithms for matrix functions, which promise a step change in scalability to very large numbers of processors and thereby significant impact on large scale applications in computational science and engineering.This research programme is ground-breaking in going beyond the state of the art across the whole range of matrix functions research from theory to software. The expected impact is high both within the field and in the many applications areas that will benefit from the new and improved algorithms.