Meetings

Group meetings are on Monday at 11am in Frank Adams 2. If you would like to give a presentation please contact Stephanie Lai.

Group photo (March 2020)

Forthcoming Meetings

Monday May 23, 2022

Bastien Vieuble on “Mixed precision strategies for preconditioned GMRES”.

Abstract:

The new promises of accessible and efficient hardware support for very low precision arithmetics are a potential source for major performance improvements in scientific computing. However, exploiting such low arithmetic precisions while keeping a satisfactory accuracy on the solution leads to rethink our algorithms within a mixed precision setting. In this talk, we particularly focus on the use of mixed precision inside preconditioned GMRES for the solution of linear systems. We will cover the state of the art on the topic and we will develop new strategies consisting in applying the matrix-vector products with the original matrix A and the preconditioner in two different precisions. In particular, in some cases, the preconditioner can be applied in a lower precision than the matrix-vector product with A, leading to possible performance improvement when the application of the preconditioner is the dominant operation in an iteration of GMRES. We will demonstrate why and when this strategy makes sense by carrying a rounding error analysis on the algorithm and by providing numerical experiments using different preconditioners in Julia.

Past Meetings

Monday May 16, 2022

Nick Higham on “Creativity and Iterative Refinement”.

Monday May 9, 2022

Marcus Webb on “Randomized Preconditioning”.

Monday April 25, 2022

Alban Boor Riley on “The inverse eigenvalue problem in spin spectroscopy”.

Monday March 28, 2022

Nick Higham on “Probabilistic Rounding Error Analysis of Householder QR Factorization”.

Monday March 14, 2022

Bastien Vieuble on “Combining sparse approximate factorizations with mixed precision iterative refinement”.

Abstract:

Iterative refinement is seeing its popularity growing again with the new promises of accessible and efficient hardware support for half precision arithmetics. Novel variants of this methods were recently proposed that rely either on the LU factorization or a LU-preconditioned GMRES method for the solution of the correction equation and can employ up to three precisions. The effectiveness of these methods was extensively proved on dense linear systems but the case of sparse problems was not studied as much. Our work aims to fill this gap. First, we have extended the theoretical ground and proposed novel variants that can employ up to five precisions concurrently. Furthermore, we have studied the use of approximation techniques that are commonly used to improve the performance and scalability of sparse direct methods. In all cases we derived theoretical bounds for the convergence conditions and the associate solution accuracy. Second we have implemented these variants on top of a parallel sparse direct solver. We will present the performance of the algorithms on large, sparse problems coming from a variety of real-life and industrial applications showing that the proposed approach can lead to considerable reductions of both the time and memory consumption.

Monday February 21, 2022

Mantas Mikaitis on “Numerical Behavior of GPU Matrix Multiply-Accumulate Hardware”.

Monday February 14, 2022

Ian Mcinerney on “Numerical Methods for Model Predictive Control”.

Monday December 20, 2021

Ayana Mussabayeva on “Classification of EEG features in Brain-Computer Interface Speller”.

Monday December 13, 2021

Nick Higham on “Logarihtmic Norms”.

Monday November 22, 2021

Stefan Güttel on “CLASSIX: fast and explainable clustering based on sorting“.

Monday November 08, 2021

Xinye Chen on “An efficient aggregation method for the symbolic representation of

temporal data”.

Monday November 01, 2021

Nick Higham on “Matrix Norms”.