Functions of Matrices: Theory and Computation

This is a five-year research project (2011-2016) funded by an ERC Advanced grant (MATFUN, 2M euros) under the direction of Professor Nick Higham.

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.

Topics of investigation include

  • nonprimary functions, structured matrices, and nonnormality,
  • new and improved algorithms for evaluating various matrix functions as well as their Fréchet derivatives and condition numbers,
  • the f(A)b problem of computing the action of a matrix function on a vector,
  • asynchronous algorithms for parallel computation of matrix functions,
  • the interplay of all the above with applications including networks, Markov processes, numerical solution of differential equations and computer graphics.

People involved

Researchers funded by the project:

Other researchers contributing to the project:



The group meets weekly, either for a matrix function group meeting or in the numerical linear algebra group meeting.

A variety of PhD and postdoctoral positions are available in the group. See the page Numerical Linear Algebra Group: Opportunities for current details.

Publications from the project can be found among the numerical analysis group ePrints.

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