Numerical Linear Algebra Group

Nick Higham is Royal Society Research Professor and Richardson Professor of Applied Mathematics. His research focuses on the development of algorithms, primarily in numerical linear algebra, and analysis of their accuracy and stability. Current research topics include functions of matrices, rounding error analysis, and matrix nearness and completion problems. In particular, he is developing effective mixed precision algorithms that exploit GPUs and other many-core processors. Nick is a Fellow of the Royal Society, a SIAM Fellow, and a Member of Academia Europaea. He publishes a blog about applied mathematics.

Françoise Tisseur is Professor of Numerical Analysis and Director of the Manchester Institute of Mathematical Sciences. Her work focuses on nonlinear eigenvalue problems and structured matrix problems, including the development of algorithms and software. She is a member of the editorial boards of the SIAM Journal on Matrix Analysis and Applications and the IMA Journal of Numerical Analysis. She is a SIAM Fellow.

Jack Dongarra holds appointments at the University of Tennessee, Oak Ridge National Laboratory, and the University of Manchester. He specializes in numerical algorithms in linear algebra, parallel computing, use of advanced-computer architectures, programming methodology, and tools for parallel computers. He received the 2021 ACM A.M. Turing Award. Other awards include the SIAM Special Interest Group on Supercomputing’s award for Career Achievement in 2010; the IEEE Charles Babbage Award in 2011; the ACM/IEEE Ken Kennedy Award in 2013; the SIAM/ACM Prize in Computational Science and Engineering in 2019; and the IEEE Computer Society’s Computer Pioneer Award in 2020. He is a Foreign Member of the Royal Society, a member of the US National Academy of Engineering, a foreign member of the Russian Academy of Science, and a Fellow of the AAAS, ACM, IEEE, and SIAM.

Sven Hammarling is currently a Senior Honorary Research Fellow. He is a SIAM Fellow and an IMA Fellow.

Stefan Güttel is Professor of Applied Mathematics. His work focuses on computational mathematics, including numerical algorithms for large-scale linear algebra problems arising with differential equations and in data science. He is Associate Editor for the SIAM Journal on Scientific Computing and Electronic Transactions on Numerical Analysis. He has been awarded the 2021 SIAM James H. Wilkinson Prize in Numerical Analysis and Scientific Computing, a 2018 Manchester Teaching Excellence Award, and holds a Fellowship with the Turing Institute.

Marcus Webb is a Lecturer in Applied Mathematics. His research grapples with foundational aspects of the numerical solution of differential equations, in particular approximation theory and numerical linear algebra. On the numerical linear algebra side, his interests lie in extremely ill conditioned least squares problems and infinite dimensional spectral problems.

Research Associates

Chris Hickey is a Knowledge Transfer Partnership (KTP) Associate working with Arup in collaboration with the Numerical Linear Algebra Group. His work aims to develop and embed leading edge algorithms from numerical linear algebra into Arup’s next generation software for structural engineering simulation. Alongside this, he is currently finishing his PhD in computer science with the University of Warwick, after previously doing his undergrad at Warwick’s Institute of Mathematics. His research at Warwick covered streaming interactive proofs and cryptographic zero knowledge protocols. At Arup, his principle work is on sparse eigenvalue problems.

Ian McInerney obtained a BSc(Hons) and an MSc in Electrical Engineering from Iowa State University in Ames, IA, USA in 2015 and 2017, respectively, and a PhD in High Performance Embedded and Distributed Systems in 2022 from the Centre for Doctoral Training in High Performance Embedded and Distributed Systems (the HiPEDS CDT) at Imperial College London under the supervision of Prof. Eric Kerrigan and Prof. George Constantinides. His research interest encompases the fields of control theory, optimization, numerical analysis, and computer architecture, with his doctoral research investigating the implementation and analysis of numerical methods for model predictive control on embedded systems. His current research focuses on the analysis and implementation of numerical methods using low-precision arithmetic.

Mantas Mikaitis obtained a BSc(Hons) and a PhD in computer science from the University of Manchester in 2016 and 2020 respectively. In his studies he worked on the SpiNNaker project led by Prof. Steve Furber and, under the supervision of David R. Lester, explored numerical accuracy of neural simulations on the SpiNNaker neuromorphic chip and has developed arithmetic accelerators for the next generation SpiNNaker2 chip. In 2019 he received a prestigious EPSRC Doctoral Prize Fellowship as part of which he is researching low precision arithmetic in numerical linear algebra. His research interests include various aspects of computer arithmetic and related topics.

PhD Students

Alban Bloor Riley is a PhD student working with Marcus Webb and Mike Baker (from the Chemistry Department). His research focusses on developing new algorithms for solving the inverse eigenvalue problem associated with neutron spin spectroscopy experiments.

Xinye Chen is a third-year Ph.D. student supervised by Prof. Stefan Güttel. His research interests include the Krylov subspace and time series analysis, with a particular interest in the application of accelerated matrix computation​. He is currently working on topics in graph representation learning and pattern recognition. 

Michael Connolly is a third year PhD student working with Professor Nick Higham. His research focuses on developing a new generation of numerical linear algebra algorithms that exploit current and future computers. He has a particular interest in multi-precision arithmetic, stochastic rounding and randomized algorithms.

Xiaobo Liu is a third year PhD student, supervised by Professor Nick Higham. His research focuses on computing functions of matrices in multi-precision arithmetic, which is concerned with algorithms for evaluating matrix functions in the arithmetic of precisions beyond the standard single and double. In particular, this includes the half-precision arithmetic that is becoming prevalent on GPUs and arbitrary precision arithmetic.

Ayana Mussabayeva is a first year PhD student, supervised by Professor Stefan Güttel and Professor Igor Larossa. Before starting her PhD, she was conducting a research in machine learning and signal processing in brain-computer interfaces. Her current research focuses on developing new machine learning approaches to learn parameters in ordinary differential equations from chemical reactions’ data. 

Thomas Seleiro is a first year PhD student, supervised by Professor Nick Higham and Professor Françoise Tisseur. His research interests include developing faster linear algebra algorithms, in particular algorithms that take advantage of computer parallelism and use low precision floating point arithmetic.

External Members

Massimiliano Fasi is assistant professor in computer science at Durham University. He develops algorithms for solving linear algebra problems at scale on parallel machines with heterogenous architectures. His work mostly focuses on the evaluation of matrix functions and the solution of matrix equations. Other research interests include matrix theory and computer arithmetic.

Ramaseshan Kannan is a senior engineer at Arup, where he develops simulation software for structural analysis. His work covers algorithm development, mathematical modelling, linear algebra solvers, software performance optimisation, data structures and parallel programming, and technology transfer. Research interests include matrix algorithms, structural dynamics, sparse linear algebra, and the applications of machine learning in engineering simulation. Ramaseshan is an alumnus of the NLA group and manages ongoing collaborations and sponsored research initiatives with the School of Maths.

Craig Lucas is the Director of the Core Software Group UK at AMD and leads a team of Mathematical, Machine Learning and High Performance Computing programmers and code optimizers. Along with their international colleagues they produce high performant software for AMD CPU architectures, including AOCL and ZenDNN.

Since graduating from this group with a PhD in Numerical Linear Algebra in 2004 he has worked on many joint projects with the school including MSc, PhD and Knowledge Transfer Partnerships (KTP).

Theo Mary is a CNRS researcher at the LIP6 laboratory in Paris, France. His research focuses on the design and development of high performance parallel numerical algorithms, and on their error and complexity analyses. In particular, he is investigating the use of mixed precision arithmetic and/or low rank approximations to accelerate numerical linear algebra algorithms on modern supercomputers.

Elisa Riccietti is currently associate professor at Ecole Normale Superieure in Lyon, France. Her research revolves around numerical optimization and machine learning. In the past her research focused on the solution of least-squares problems with noisy function and gradient, in particular ill-posed large-scale problems with inexact function and gradient. More recently she is working on the application of multilevel optimization methods to the training of artificial neural networks and on momentum-based second order methods for machine learning. 

Eleni Vlachopoulou is a senior software engineer at AMD since April 2022 and is part of the Numerical Software team. She obtained her MSc in Applied Mathematics with Numerical Analysis from the University of Manchester in 2018. In January 2019, she joined NAG Ltd., where she worked on high performance numerical software projects, with a focus on linear algebra solvers, such as sparse linear systems and dense SVD and eigenvalue decompositions, and Automatic Differentiation (AD).

Mawussi Zounon is a senior software engineer at Arm Manchester since June 2021. In this role, he is working on the design and optimisation of Arm Radio Access Network (RAN) acceleration libraries for Arm customers deploying 5G solutions. He joined the Numerical Linear Algebra Group in January 2016 as a postdoctoral research fellow on the NLAFET (Parallel Numerical Linear Algebra for Extreme Scale Systems) project. At the end of the NLAFET project, he continued working with the Numerical Linear Algebra Group as a Knowledge Transfer Partnership (KTP) associate, in partnership with NAG. The aim of the KTP project was to develop new numerical linear algebra routines for NAG software to exploit emerging computer architectures. He received an Engineering degree in computation science in 2011 from the Polytechnic Institute of Bordeaux in France, and a PhD in applied mathematics and computer science in 2015 from the University of Bordeaux for his contribution to numerical fault tolerant strategies for large sparse linear algebra solvers with a special focus on Krylov subspace methods.