Group meetings are on Thursday at 11am in Frank Adams 1. If you would like to give a presentation please contact Stephanie Lai.

Past Meetings

Wednesday September 11

Theo Mary on “Numerical Stability of Block Low-Rank LU Factorization”.
Abstract: Block low-rank (BLR) matrices exploit blockwise low-rank approximations to reduce the complexity of numerical linear algebra algorithms. The impact of these approximations on the numerical stability of the algorithms in floating-point arithmetic has not previously been analyzed. We present rounding error analysis for solution of a linear system by LU factorization of BLR matrices. We prove backward stability, assuming that a stable pivoting scheme is used, and obtain new insights into the numerical behavior of BLR variants. We show that the predictions from the analysis are realized in practice by testing them numerically on a wide range of matrices coming from various real-life applications.

Wednesday July 31

Elisa Riccietti on “On the iterative solution of systems of the form A^TAx=A^Tb+c”. Abstract, Sildes.

Wednesday June 19

Theo Mary on “Sharper and smaller rounding error bounds for low precision scientific computing”.

Wednesday May 22

Conor Rogers on “Some experiments on rational approximation with noisy data”. Slides

Wednesday May 8

Florent Lopez on “Performance and accuracy of the LU factorisation on GPU using Tensor Cores”.
Abstract: We currently observe an emergence of new hardware supporting low precision floating-point formats, such as the IEEE half precision format. This is for example the case of recent NVIDIA GPUs such as the Volta and Turing architectures that dramatically improve the performance of half-precision computations with the introduction of new processing units called Tensor Cores. In this talk we discuss the use of Tensor cores  for performing a reduced precision LU factorisation and we show the benefits of exploiting such processing units both in terms of performance and accuracy compared to traditional single and half precision variants.

Wednesday May 1

Srikara Pranesh on “Simulating Low Precision Floating-Point Arithmetic”.

Wednesday April 3

Michael Connolly on “Multiprecision Inverse Computation”. Slides.
Abstract: In this talk we discuss the Newton-Schulz iteration for computing the generalized inverse of a matrix. We discuss numerical results arising from a multiprecision implementation of this algorithm as well as the use of a low precision solution to this problem as a preconditioner for mixed precision iterative refinement.

Wednesday March 27

Xiaobo Liu on “Computing the Matrix Mittag-Leffler Function”. Slides.
Abstract: Similar to the matrix exponential in the solutions of linear differential equation systems, the matrix Mittag-Leffler (ML) function plays an analogous role in solving linear fractional differential equation systems, which have been proved to be the best way of modelling many physical and engineering processes in real life. In this talk, I will mainly review a recent paper for computing the matrix ML function based on the Schur-Parlett algorithm.

Wednesday March 19

Mawussi Zounon will give a talk about PLASMA and the NAG Library.

Wednesday March 13

Xuelei Lin from Hong Kong Baptist University
Title: Crank-Nicolson ADI method for space-fractional diffusion equations with non-separable coefficients
Abstract: Alternating direction implicit (ADI) scheme is a popular and efficient solver for linear systems arising from discretization of high-dimension fractional PDEs. However, ADI schemes developed in previous works requires strong assumptions, such as separable coefficients, or even constant coefficients. In this talk, I will introduce our newly developed theory for Crank-Nicolson ADI, which does not require separable-coefficients assumptions. Also, an optimal preconditioning technique is applied to the one-dimensional problems arising from ADI scheme, for which the condition number of the preconditioned matrices are proven to be independent of discretization step-sizes.

Wednesday March 6

Chris Armstrong from Arm
Title: Arm Performance Libraries FFT development
Abstract: In this talk I will give a quick overview of Arm Performance Libraries before describing the work we have undertaken to improve the performance of our Fast Fourier Transform (FFT) functions. I will outline the algorithms we use and our results to date.

Wednesday January 30

Pierre Blanchard on “Yet Another Fast And Accurate Summation Algorithm”.

Wednesday January 23

Sven Hammarling on “Machines for the Solution of Linear Equations”. NotesSlides and References.

Tuesday December 11

Massimiliano Fasi on “Efficient and Accurate evaluation of polynomials of matrices”. Notes and Slides.

Tuesday December 4

Theo Mary on “A New Approach to Rounding Error Analysis”. Paper and Slides.

Tuesday November 20

Lijing Lin on “Phenotyping immune responses in asthma and respiratory infections using clustering techniques”.  An abstract for the talk is available here.

Tuesday November 13

Srikara Pranesh on “Squeezing a Matrix Into Half Precision, with an Application to Solving Linear Systems”.

Tuesday November 6

Elisa Riccietti on “High-order multilevel optimization strategies and their application to the training of artificial neural networks”. Abstract for the talk is available here.

Tuesday October 30

Gain Maria Negri Porzio on “The contour integral approach for the nonlinear eigenvalue problem”.

Tuesday October 23

Nick Higham on “The adjugate matrix”. From the meeting: Notes.

Tuesday October 16

Tom McSweeney on ”Task scheduling in high-performance computing”. From the meeting: Slides, Notes.

Tuesday October 9

Nick Higham on ”Optimizing the Wilson Matrix”. From the meeting: Notes.

Here is the group photo from the meeting (hires version).DSC00120.ARW

Tuesday October 2

Pierre Blanchard on ”Optimized Polar Decomposition for Modern Computer Architectures”. From the meeting: Slides, Notes.

Tuesday September 25

Introductions, new website, and plans for the academic year, including conferences. From the meeting: Notes.