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Department of Mathematics

Approximation theory

Approximation theory is a key component of contemporary algorithms used in computational science and engineering.

The mathematical theory underlying approximation has a crucial role in the design of efficient computational algorithms for representing real-life data and the numerical solution of differential equations, by providing insight into the computational cost associated with a desired error. We look at both practical and theoretical aspects of the subject. Our work has links with many other areas of mathematics, as well as science, engineering and medical research.

Many of our projects are interdisciplinary and produce open source computer code used by researchers in other disciplines.

We are actively engaged in research projects related to a wide range of topics, including:

  • Frame-based discretisation of differential equations
  • Spectral approximation methods
  • Finite difference methods for fractional Laplacians
  • Finite element methods for PDEs with random data
  • Nonlinear rational approximation

More information about our research outputs and research-related activities can be found by browsing the webpages of the staff listed on the right. Potential PhD students may email academic staff directly to discuss possible projects.