About the Project
Modern scientific computing and data analysis increasingly involve matrices that are too large for traditional numerical algorithms to handle efficiently. Randomized numerical linear algebra addresses this challenge by using random sampling and sketching to construct smaller problems that retain the important information in the original data.
At the same time, modern CPUs and GPUs increasingly provide very fast arithmetic at reduced precision, driven in part by developments in artificial intelligence. This PhD project will explore how these two rapidly developing areas, randomized algorithms and mixed-precision computing, can be combined to design faster and more efficient numerical methods without sacrificing the accuracy and reliability required in scientific computing.
The student will develop and analyse new algorithms for problems such as low-rank approximation, least squares, and eigenvalue or singular value computation. The project will combine mathematical analysis, algorithm design, and computational experiments, providing training at the interface of numerical linear algebra, randomized algorithms, and high-performance scientific computing.
This project is expected to start in September 2027.
Before you apply: We strongly recommend that you contact the supervisors for this project before you apply.
How to apply: To be considered for this project you must complete a formal application through our online application portal. If you already have an applicant account this link will directly open an application for PhD School of Natural Sciences Scholarships. If you don’t already have an applicant account, please follow the instructions here.
When applying, please specify the full title and supervisor/s of the project, details of your previous study, and names and contact details of two referees. You must also upload a Supporting Statement describing your motivation to apply to the project, your CV and transcripts of awarded and in-progress university qualifications. Please note late or incomplete applications will not be considered.
Equality, diversity and inclusion are fundamental to the success of The University of Manchester and central to all our activities. A diverse research community strengthens creativity, productivity and quality, while increasing the societal and economic impact of our work. We welcome applicants from all career paths, backgrounds and sections of the community, regardless of age, disability, ethnicity, gender, gender expression, sexual orientation or transgender status.
We welcome applications from candidates returning to study after a career break or experience in other roles. Flexible study arrangements may be available, including part-time study at 50%, 60% or 80%, subject to the requirements of the project and funder.
Eligibility: The standard academic entry requirement for this PhD is an upper second-class (2:1) honours degree (or international equivalent) in a Mathematics or a closely related discipline OR any upper-second class (2:1) honours degree and a Master’s degree at merit (or international equivalent) in Mathematics or a closely related discipline.
This project will remain open until filled.
If your application is submitted by 1st November 2026, you can expect a decision by 18th December 2026.
If your application is submitted by 15th January 2027, you can expect a decision by 30th March 2027.
Self or externally funded students can also be considered for this project.
FSE_SoNS
Funding Notes
Funding covers tuition fees, an annual stipend at the UKRI minimum rate (currently £21,805 per year), and a research training support grant of up to £2,500 per year for the full 3.5-year programme.