Mixed precision methods for numerical linear algebra at exascale

Join an international team developing scalable algorithms to solve numerical linear algebra challenges on supercomputers.<br /> <br /> Modern high-performance computing increasingly relies on hardware accelerators originally designed for artificial intelligence. These accelerators achieve exceptional performance by using low precision arithmetic, which is sufficient for machine learning tasks but much too inaccurate for most scientific applications. To harness these accelerators for scientific computing, one must develop new algorithms that combine low and high precision computations in a way that preserves accuracy while delivering significant gains in terms of speed and energy efficiency.<br /> <br /> This PhD project will focus on developing mixed precision algorithms for large scale, sparse eigenvalue problems and matrix functions. These computational problems are central to many scientific and engineering applications, including quantum mechanics, materials science, and weather and climate modelling. Numerical methods currently available cannot fully exploit modern accelerators, and are therefore not suitable to run on todays largest supercomputers. By redesigning these algorithms for mixed precision, the project aims to deliver robust, scalable solutions that will eventually be integrated into widely used scientific software libraries.<br /> <br /> The successful candidate will join a dynamic research environment and gain access to state of the art supercomputers. There will be opportunities to collaborate with researchers at the University of Leeds, the Rutherford Appleton Laboratory, a UK National Lab in Oxfordshire, and Environment and Climate Change Canada, the Canadian counterpart of the Met Office. The algorithms developed during the PhD will become part of SLEPc (the Scalable Library for Eigenvalue Problem Computations, hosted at the Universitat Politecnica de València) and SLATE (Software for Linear Algebra Targeting Exascale, hosted at the University of Tennessee at Knoxville).<br /> <br /> Applicants should have a strong interest in numerical algorithms and scientific computing. A background in applied mathematics, computational mathematics, computer science, physics, or engineering is suitable. Basic programming experience (e.g., C, C++, Julia, MATLAB, Python, or similar) is necessary; knowledge of numerical linear algebra or high performance computing is desirable but not essential. Training will be provided.<br /> <br /> By the end of the PhD, the student will have gained knowledge and experience in numerical analysis, with a particular focus on linear algebra, and in high performance computing. There will be opportunities to present research at national and international conferences, work on scientific publication, and contribute to widely used scientific software libraries.

<p>Formal applications for research degree study should be made online through the <a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University's website</a>. Please state clearly in the <em><strong>Planned Course of Study section that you are applying for PHD Computer Science FT</strong></em>, in the research information section, please state clearly that the research project you wish to be considered for is <em><strong>Mixed precision methods for numerical linear algebra at exascale</strong></em>, and mention <a href="https://eps.leeds.ac.uk/computing/staff/14034/massimiliano-fasi">Dr Massimiliano Fasi</a> as your proposed supervisor and in the finance section, please state clearly that you are applying for the <em><strong>School of Computer Science Scholarship 2025/26 (EPSRC Grant: Mixed Precision).</strong></em></p> <p>If English is not your first language, you must provide evidence that you meet the University's minimum English language requirements (below).</p> <p>Applications will be considered on an ongoing basis.  Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application.  We also advise that you apply at the earliest opportunity as the application and selection process may close early, should we receive a sufficient number of applications or that a suitable candidate is appointed.</p> <p>Please ensure you provide your supporting documents by the closing date of Monday 17 November 2025: </p> <ul> <li>Full Transcripts of all degree study or if in final year of study, full transcripts to date including grading scheme</li> <li>Personal Statement outlining your interest in the project</li> <li>CV</li> </ul> <p><em>As an international research-intensive university, we welcome students from all walks of life and from across the world. We foster an inclusive environment where all can flourish and prosper, and we are proud of our strong commitment to student education. Across all Faculties we are dedicated to diversifying our community and we welcome the unique contributions that individuals can bring, and particularly encourage applications from, but not limited to Black, Asian, people who belong to a minority ethnic community, people who identify as LGBT+ and people with disabilities. Applicants will always be selected based on merit and ability.</em></p>

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid. Some schools and faculties have a higher requirement.

<p class="MsoNoSpacing">A highly competitive School of Computer Science Studentship, in support of the EPSRC Grant: Mixed precision in Krylov Methods, providing the award of full academic fees, together with a tax-free maintenance grant at the standard UKRI rate (£20,780 in academic session 2025/26) for 3.5 years. There are no additional allowances for travel, research expenses, conference attendance or any other costs.<br /> <br /> You will be responsible for paying the overtime fee in full in your writing up/overtime year (£340 in Session 2025/26), but the scholarship maintenance allowance will continue to be paid for up to 6 months in the final year of award.</p> <p>Please note that there is only 1 funded place available to UK applicants only.  If you are successful in securing an academic offer for PhD study, this does not mean that you have been successful in securing an offer of funding.</p> <p>Please refer to the <a href="https://www.ukcisa.org.uk/">UKCISA</a> website for information regarding Fee Status for Non-UK Nationals.</p>

<p>For further information about this project, please contact Massimiliano Fasi at <a href="mailto:m.fasi@leeds.ac.uk?subject=%5BPhD%20contact%5D%20Computer%20arithmetic%20for%20the%20next%20generation%20of%20integrated%20circuits">M.Fasi@leeds.ac.uk</a>.</p> <p>For further information about your application, please contact the Postgraduate Research Admissions team at <a href="mailto:phd@engineering.leeds.ac.uk">phd@engineering.leeds.ac.uk</a>.</p>