Numerical Linear Algebra Group

Sixteen publications by members of the NLA group feature among the top 40 most read articles in two SIAM journals, both leading venues for publications in numerical linear algebra. 

The following articles are amongst the 20 most read in the SIAM Journal on Matrix Analysis and Applications:

• Matrix Inverse Trigonometric and Inverse Hyperbolic Functions: Theory and Algorithms by Mary Aprahamian and Nicholas J. Higham
• An Arbitrary Precision Scaling and Squaring Algorithm for the Matrix Exponential by Massimiliano Fasi and Nicholas J. Higham
• Higher Order Fréchet Derivatives of Matrix Functions and the Level-2 Condition Number by Nicholas J. Higham and Samuel D. Relton
• Generalized Rational Krylov Decompositions with an Application to Rational Approximation by Mario Berljafa and Stefan Güttel
• The Structured Condition Number of a Differentiable Map between Matrix Manifolds, with Applications by Bahar Arslan, Vanni Noferini, and Françoise Tisseur
• An Algorithm for the Matrix Lambert $W$ Function by Massimiliano Fasi, Nicholas J. Higham, and Bruno Iannazzo
• The Block Rational Arnoldi Method by Steven Elsworth and Stefan Güttel
• Multiprecision Algorithms for Computing the Matrix Logarithm by Massimiliano Fasi and Nicholas J. Higham

The following articles are amongst the 20 most read in the SIAM Journal on Scientific Computing:

• Accelerating the Solution of Linear Systems by Iterative Refinement in Three Precisions by Erin Carson and Nicholas J. Higham
• A New Approach to Probabilistic Rounding Error Analysis by Nicholas J. Higham and Theo Mary
• Simulating Low Precision Floating-Point Arithmetic by Nicholas J. Higham and Srikara Pranesh
• A New Analysis of Iterative Refinement and Its Application to Accurate Solution of Ill-Conditioned Sparse Linear Systems by Erin Carson and Nicholas J. Higham
• Shifted Cholesky QR for Computing the QR Factorization of Ill-Conditioned Matrices by Takeshi Fukaya, Ramaseshan Kannan, Yuji Nakatsukasa, Yusaku Yamamoto, and Yuka Yanagisawa
• Squeezing a Matrix into Half Precision, with an Application to Solving Linear Systems by Nicholas J. Higham, Srikara Pranesh, and Mawussi Zounon
• A Class of Fast and Accurate Summation Algorithms by Pierre Blanchard, Nicholas J. Higham, and Theo Mary
• Estimating the Largest Elements of a Matrix by Nicholas J. Higham and Samuel D. Relton

The full lists (updated daily) are available here and here. 

Professor Françoise Tisseur has been awarded the London Mathematics Society’s Fröhlich Prize for “her important and highly innovative contributions to the analysis, perturbation theory, and numerical solution of nonlinear eigenvalue problems”.

The Fröhlich Prize is awarded even two years in memory of Albrecht Fröhlich, FRS. The prize is awarded for original and extremely innovative work in any branch of mathematics.

The full prize citation is available here.

Professor Nick Higham is featured in the June 2020 issue of The Actuary Magazine, the magazine of the Institute and Faculty of Actuaries.

In an interview with the editor, Dan Georgescu, Nick talks about his development in 2002 of his nearest correlation matrix algorithm, which is widely used in finance and data science.

The magazine is freely readable on the Issuu platform.

More details about the nearest correlation matrix problem and algorithms for solving it are available on Nick’s blog.

Dr Stefan Güttel is one of the organizers of a new online series of seminars on Numerical Linear Algebra. The talks are broadcast live on Zoom and YouTube every Wednesday at 4pm Central European Summer Time (CEST). The programme is available on the seminar website. At the time of writing, 942 people from 79 countries have signed up to the seminar mailing list.

The other organizers are Melina Freitag (University of Potsdam), Daniel Kressner (EPF Lausanne), Jörg Liesen (TU Berlin), Valeria Simoncini (University of Bologna), and Bart Vandereycken (University of Geneva).

The first talk in the series was given by Professor Nick Higham, titled Are Numerical Linear Algebra Algorithms Accurate at Extreme Scale and at Low Precisions? The slides for the talk are available at this link and the video is below.

This year’s group photo was taken on March 5, 2020 after the NLA group meeting. Most group members are in the photo; those missing include Jack Dongarra, Stefan Güttel, Ramaseshan Kannan and Marcus Webb. 

The banner on this website has also been updated with the new group photo.  A high resolution version of the photo is available here.

By row from the back: Craig Lucas, Nick Higham, Xinye Chen, Steven Elsworth, Xiaobo (Bob) Liu, Michael Connolly, Mantas Mikaitis, Len Freeman, Massimiliano Fasi, Pierre Blanchard, Sven Hammarling, Asad Raza Aitor Mehasi Mehasi, Stephanie Lai, Gian Maria Negri Porzio, Thomas McSweeney Mawussi Zounon, Françoise Tisseur, Srikara Pranesh, Yuqing (Mila) Zhang, Eleni Vlachopoulou.

Several members of the group attended the SIAM Conference on Parallel Processing for Scientific Computing held in Seattle on February 12-15, 2020.

The presentations given are as follows:

• Fast Generation of Extreme-Scale Matrices with Preassigned 2-Norm Condition Number by Massimiliano Fasi
• Solving Neural ODEs using Fixed-Point Arithmetic with Stochastic Rounding by Mantas Mikaitis
• Low Precision Floating-Point Arithmetic for the Solution of Linear System of Equations by Srikara Pranesh
• Opportunities for Multi Precision Computation in Memory Bound Applications by Mawussi Zounon
• Performance and Accuracy of Mixed-Precision Matrix Factorizations with GPU Tensor Cores by Theo Mary (alumnus).

Nick Higham and Srikara Pranesh also organised a two part mini-symposium (Advances in Algorithms Exploiting Low Precision Floating-Point Arithmetic, MS10 and MS21) at the conference. 

Max Fasi, Mantas Mikatis, Mawussi Zounon, Sri Pranesh, Theo Mary at SIAM Conference on Parallel Processing for Scientific Computing, Seattle, Washington, February 12-15, 2020.

by Sven Hammarling, Nick Higham, and Françoise Tisseur

Jack Dongarra

July 18, 2020 is the 70th birthday of Professor Jack Dongarra, who holds appointments at the University of Tennessee, Oak Ridge National Laboratory, and the University of Manchester.

Jack has made seminal contributions to algorithms for numerical linear algebra and the design and development of high performance mathematical software for machines ranging from workstations to the largest parallel computers. His recent honours include election as a Foreign Member of the Royal Society and receipt of the
SIAM/ACM Prize in Computational Science and Engineering (2019)and the IEEE Computer Society Computer Pioneer Award (2020).

To celebrate Jack’s birthday we are organizing a conference New Directions in Numerical Linear Algebra and High Performance Computing: Celebrating the 70th Birthday of Jack Dongarra at The University of Manchester, July 17, 2020.  Registration is now open and we welcome submission of posters.

Professors Jack Dongarra and Nick Higham, together with Dr Laura Grigori (Inria Paris), have edited the issue Numerical Algorithms for High-Performance Computational Science of the journal Philosophical Transaction of The Royal Society A. The issue is now available online.

The issue contains papers from a Discussion meeting of the same title organized at the Royal Society in April 2019.  A report on that meeting, along with photos from it, is available here.  The content of the issue, with links to the papers, is as follows.

Table of Contents

Numerical algorithms for high-performance computational science by Jack Dongarra, Laura Grigori and Nicholas J. Higham.

The future of computing beyond Moore’s Law by John Shalf.

Hierarchical algorithms on hierarchical architectures by D. E. Keyes , H. Ltaief and G. Turkiyyah.

Stochastic rounding and reduced-precision fixed-point arithmetic for solving neural ordinary differential equations by Michael Hopkins, Mantas Mikaitis, Dave R. Lester and Steve Furber.

Preparing sparse solvers for exascale computing by Hartwig Anzt, Erik Boman, Rob Falgout et al.

On the cost of iterative computations by Erin Carson and Zdeněk Strakoš.

Rethinking arithmetic for deep neural networks by G. A. Constantinides.

Machine learning and big scientific data by Tony Hey , Keith Butler, Sam Jackson and Jeyarajan Thiyagalingam.

The physics of numerical analysis: a climate modelling case study by T. N. Palmer.

Exascale applications: skin in the game by Francis Alexander, Ann Almgren, John Bell et al.

Big telescope, big data: towards exascale with the Square Kilometre Array by A. M. M. Scaife.

Optimal memory-aware backpropagation of deep join networks by Olivier Beaumont, Julien Herrmann, Guillaume Pallez (Aupy) and Alena Shilova.

High-performance sampling of generic determinantal point processes by Jack Poulson.

A survey of algorithms for transforming molecular dynamics data into metadata for in situ analytics based on machine learning methods by Michela Taufer , Trilce Estrada and Travis Johnston.

The parallelism motifs of genomic data analysis by Katherine Yelick , Aydın Buluç, Muaaz Awan et al.

Jack Dongarra

Professor Jack Dongarra, a member of the Manchester Numerical Linear Algebra Group who also holds appointments at the University of Tennessee  and Oak Ridge National Laboratory, has been named as recipient of the IEEE Computer Society’s 2020 Computer Pioneer Award.

The award is given for significant contributions to early concepts and developments in the electronic computer field that have clearly advanced the state-of-the-art in computing.  Dongarra is being recognized “for leadership in the area of high-performance mathematical software.”

Dongarra will receive his award at the Computer Society’s annual awards dinner and presentation to be held on Wednesday 27 May 2020 at the Hilton McLean Tysons Corner during the IEEE Computer Society Board of Governors meeting. The award consists of a silver medal and an invitation to speak at the award presentation.

This article is based on an IEEE news release. Further information about the award is available here.

Group photo at SIAM UKIE 2020

Several members of the group attended the SIAM UKIE Section Meeting held at the University of Edinburgh on Friday January 10, 2020. Françoise Tisseur, President of the Section and one of the co-organizers, chaired the morning session.

PhD students Michael Connolly,  Xiaobo (Bob) Liu, Gian Maria Negri Porzio, and Research Associate Srikara Pranesh presented posters.

Congratulations to Sri and Michael, who won first and second best poster prizes, respectively:
a cheque for £75 to both and also a copy of the book /50 Visions of Mathematics/ to Sri.

Xiaobo (Bob) Liu

Srikara Pranesh

Michael Connolly

Gian Maria Negri Prozio

Photo credit to Gian Maria Negri Porzio