Mixed precision methods for numerical linear algebra at exascale

About the project

About the Project Please note the start date for this project is Monday 1 February 2027. Join an international team developing scalable algorithms to solve numerical linear algebra challenges on supercomputers. 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. This PhD project will focus on developing mixed-precision algorithms for large-scale numerical linear algebra problems. Numerical methods currently available cannot fully exploit modern hardware accelerators, and they are therefore not suitable to run on todays largest supercomputers. The goal of the project is to redesign some of these algorithms for mixed precision, to deliver robust, scalable solutions that will eventually be integrated into widely used scientific software libraries. 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 meteorological service. 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 MAGMA (Matrix Algebra on GPU and Multi-core Architectures, hosted at the University of Tennessee at Knoxville). 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 is desirable but not essential. 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.

Research areas