Area of investment and support

Numerical analysis

Research into the development, analysis and implementation of algorithms that harness numerical approaches to mathematical problems.

• Partners involved: Engineering and Physical Sciences Research Council (EPSRC)

The scope and what we're doing

This area encompasses research into the development, analysis and implementation of algorithms that harness numerical approaches to mathematical problems. This research area is concerned with both computational mathematics (using mathematical methodology to understand discretisation and computation) and scientific computing (designing practical computational algorithms to address challenges in all areas of science and engineering).

Numerical analysis in the UK is internationally leading and this strategy aims to maintain the quality and scale of research in this area, while promoting its impact by strengthening links with applications.

We aim to have a portfolio of numerical analysis research and skills that:

• complements work undertaken at the Alan Turing Institute, especially by contributing to the key capabilities, mathematical representations and inference and learning, and creates effective tools to understand large, complex datasets and so contributes to the data-driven economy
• strengthens interdisciplinary links with mathematical analysis, operational research, and statistics and applied probability, by exploiting mathematical sciences infrastructure to develop connections across mathematical sciences
• is integrated into other relevant disciplines to enable full exploitation of opportunities offered by evolving computational architectures and increasing processing capacity – this will make use of existing mathematical sciences infrastructure to develop deeper links with other disciplines and will maximise use of existing equipment and coordinate requirements for equipment where possible
• includes emerging leaders, with skills transcending numerical analysis and other areas such as those related to information and communication technologies (ICT) (such as machine learning, digital signal processing) and to engineering (for example fluid dynamics and aerodynamics, materials engineering, medical imaging).

Why we're doing it

Numerical algorithms are found in virtually every field of science, technology and engineering. Advances in the development, analysis and implementation of numerical algorithms have the potential to achieve scientific, economic and societal impacts beyond those achievable solely through reliance on increases in computational processing power and advanced architectures.

Having been a pioneer in numerical analysis, the UK’s research in this area remains at a very high standard, and UK numerical analysts have enjoyed considerable international recognition in recent years. The ubiquity of numerical algorithms across science, engineering, technology and industry offers considerable potential for numerical analysis to produce substantial and diverse impact through cooperation with other disciplines.

Within mathematical sciences, the difficult mathematical challenges originating in numerical analysis are the basis for ongoing intradisciplinary connections of this research area with other mathematical areas, especially mathematical analysis.

The wide relevance of research outcomes from numerical analysis means it is of considerable importance to the UK. This is underlined by the Council for Science and Technology’s recognition of a developing ‘Age of Algorithms’ and the subsequent establishment of the Alan Turing Institute for data science.

The importance of numerical analysis to the UK economy is also reflected in EPSRC’s portfolio in this research area, a very large majority of which is relevant to one or more industrial sectors (such as healthcare, financial services and information technologies).

Evidence from the Research Excellence Framework (REF) 2014 exercise suggests that the overall number of researchers working wholly or primarily in numerical analysis has increased to some extent since the International Review of Mathematical Sciences in 2010.

Continued availability of people with appropriate skill sets in the UK, however, is a concern in some sub-disciplines, and it is important that the balance of skills evolves with the changing landscape and emerging opportunities. Specifically, there is a need to develop skills in key interdisciplinary and intradisciplinary topics such as data science, optimisation, computation of multi-scale phenomena and uncertainty quantification.

View evidence sources used to inform our research strategies.

Past projects, outcomes and impact

Visualising our portfolio (VoP) is a tool for users to visually interact with the EPSRC portfolio and data relationships. Find out more about research area connections and funding for numerical analysis.

Find previously funded projects on Grants on the Web.

Last updated: 27 July 2023