Numerical analysis

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.

By the end of this Delivery Plan period, we aim to have maintained a portfolio of Numerical Analysis research and skills that:

  • Complements work undertaken at the Alan Turing Institute (Evidence source 1), especially by contributing to the key capabilities, Mathematical Representations and Inference and Learning, and creates effective tools to understand large, complex datasets and so contributing to the data-driven economy
  • Has strengthened 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. Again, this will make use of existing mathematical sciences infrastructure to develop deeper links with other disciplines and will involve maximising use of existing equipment and co-ordinating 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) (e.g. Machine Learning, Digital Signal Processing) and to engineering (e.g. Fluid Dynamics and Aerodynamics, Materials Engineering, Medical Imaging)

Contributes to EPSRC Outcomes and especially to Healthy and Connected Nation Ambitions

Highlights:

Numerical algorithms are found in virtually every field of science, technology and engineering (Evidence source 2,3,4,5,6,7). 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 quality of UK research in this area remains at a very high standard and UK numerical analysts have enjoyed considerable international recognition in recent years (Evidence source 2,3,6). The ubiquity of numerical algorithms across science, engineering, technology and industry offers considerable potential for Numerical Analysis to produce substantial and diverse impact through co-operation 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 (Evidence source 2).

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 (Evidence source 7). 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 (e.g. healthcare, financial services and information technologies).

Evidence from the Research Excellence Framework (REF) 2014 exercise suggests that overall numbers of researchers working wholly or primarily in Numerical Analysis has increased to some extent since the International Review of Mathematical Sciences in 2010 (Evidence source 4,6). Continued availability of people with appropriate skillsets 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 (Evidence source 2). 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 (Evidence source 2,3).

This area has substantial medium to long-term relevance to all Outcomes but likely to be particularly relevant to Connected and Healthy Nation. Specific Ambitions of relevance include:

C1: Enable a competitive, data-driven economy

Novel numerical approaches to data analytics enable creative insights to be gained from data which can be applied across a range of sectors.

C2: Achieve transformational development and use of the Internet of Things

Enabling more efficient data processing can improve optimisation and the development of advanced numerical algorithms.

C3: Deliver intelligent technologies and systems

This research area can enable data to be converted into physical action through advanced numerical analytical and processing techniques (including signal, image and video processing).

H1: Transform community health and care

This area can contribute through new numerical techniques for analysis of health data from multiple sources, including medical imaging, wearable sensors and ‘omics’.

H2: Improve prevention and public health

Predictive models can be improved through advanced tools for numerical data assimilation and analysis.

Research area connections

This diagram shows the top 10 connections between Research Areas within the EPSRC research portfolio. The depth of the segment relates to value of grants and the width of the segment relates to the number of grants shared by those two Research Areas. Please click to see the related Research Area rationale.

Maintain

We aim to maintain this area as a proportion of the EPSRC portfolio.

Visualising our Portfolio (VoP)
Visualising our portfolio (VoP) is a tool for users to visually interact with the EPSRC portfolio and data relationships.

EPSRC support by research area in numerical analysis (GoW)
Search EPSRC's research and training grants.

Contact Details

In the following table, contact information relevant to the page. The first column is for visual reference only. Data is in the right column.

Name: Michael Ward
Job title: Manager
Department: Mathematical Sciences
Organisation: EPSRC
Telephone: 01793 444196