Numerical Algorithms

A long-standing interest in Manchester is the design and implementation of numerical algorithms, in areas such as numerical linear algebra, nonlinear optimisation and differential equations. Modern computer architectures, including those in desktop machines, exploit a number of features in order to achieve high performance, including cache memories, hierarchical memories, and the use of multiple processors working in parallel. Algorithms need to be carefully designed and tailored in order to extract high performance, and the group has much experience in this endeavour in the area of matrix computations. Computations with large or complex data frequently rely on fast, accurate algorithms for linear systems, eigenvalues, singular values, or functions of matrices, ranging from huge sparse matrices arising in networks to dense, highly structures matrices from time series.

Numerical Analysis Research Group

Activities include organising international conferences and a Numerical Analysis and Scientific Computing seminar series, writing textbooks and research monographs, membership of editorial boards of international journals and book series, and contributing software to the NAG and LAPACK libraries and MATLAB.

Lead Researcher:

Professor Nicholas Higham

Nick is best known for his work on the accuracy and stability of numerical algorithms. He has more than 130 refereed publications on topics such as rounding error analysis, linear systems, least squares problems, matrix functions and nonlinear matrix equations, condition number estimation, and generalized eigenvalue problems. He has contributed software to LAPACK and the NAG library, and has contributed code included in the MATLAB distribution.

Nick is an investigator on the 5-year £3M EPSRC-funded project "Inference, Computation and Numerics for Insights into Cities" (ICONIC, https://iconicmath.org/), which is developing theory, methodology, and algorithms to propagate uncertainty in mathematical models of socio-economic phenomena in future cities.  He also recently held a 2M euro ERC Advanced grant on matrix functions.

Dr Stefan Güttel

Stefan's primary research interests are numerical analysis, in particular, the design and analysis of numerical algorithms for the solution of partial differential equations and related high-dimensional linear algebra problems, rational approximation, scientific computing, and parallel algorithms. He is currently devoted to rational Krylov methods for the efficient solution of Maxwell's equations and nonlinear eigenvalue problems, optimized transparent boundary conditions, and deferred correction methods. In February 2017, Stefan was awarded the People's Vote prize in the Better World Awards for his work on Predictive Alarm Analytics in collaboration with Sabisu.

Prof Françoise Tisseur

Françoise is a Professor of Numerical Analysis in the School of Mathematics. She works in numerical linear algebra and in particular on nonlinear eigenvalue problems and structured matrix problems, including the development of algorithms and software. She has contributed software to LAPACK, ScaLAPACK, and the MATLAB distribution. Tisseur was awarded the 2010 Whitehead Prize by the London Mathematical Society for her research achievements in numerical linear algebra, including polynomial eigenvalue and structured matrix problems and the 2011-2012 Adams Prize of the University of Cambridge for her work on polynomial eigenvalue problems.

Dr Martin Lotz

Martin is a Lecturer in Mathematics at the University, his research interests revolve around probabilistic and geometric methods in computational mathematics. My current work is on applications of optimization theory, dimensionality reduction in computational topology, and genomic data analysis. Previous work has included algebraic complexity theory, computational algebra and geometry, foundations of numerical analysis, and combinatorics.