Numerical Linear Algebra Group

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

Dr Stefan Güttel, Professor Nick Higham, and Professor Françoise Tisseur have been awarded a new 30-month project with Arup, a multidisciplinary engineering firm operating in all areas of built environment.

This Knowledge Transfer Partnership (KTP), funded by Arup and Innovate UK, aims to embed new matrix eigenvalue solvers into Arup’s next generation software for structural engineering simulation.

The Numerical Linear Algebra  (NLA) group team will be working with Dr Stephen Hendry and Dr Ramaseshan Kannan of Arup, along with a KTP Associate, for which the position is advertised here.

The project builds on a long history of collaboration between Arup and the NLA Group, which has  previously led to the development of “model stability analysis” in Arup’s flagship structural engineering simulation package, Oasys GSA (see the paper What is Your Structural Model Not Telling You?).

The November 2019 edition of SIAM News contains an article by Research Associate Srikara Pranesh about the growing importance of low precision floating-point arithmetic. Sri describes the opportunities provided by recent hardware and explains how new algorithms are being derived to exploit low precision arithmetic.  To read the article click the image below.

Also see Sri’s recent blog post Simulating Low Precision Floating-Point Arithmetics.

Photo provided by @ICIAMnews

Professor Nick Higham delivered an invited talk at the International Congress on Industrial and Applied Mathematics (ICIAM) on July 19, 2019, in Valencia, Spain. His talk “Exploiting Low Precision Arithmetic in the Solution of Linear Systems” reported work by Higham and his colleagues over the last three years to use the fast half precision arithmetic available on accelerators such as GPUs to speed up the solution of linear systems.  A video of the talk is available here and the slides are available here.

The talk was summarized in the Friday 19th July edition of the ICIAM2019 newsletter:

“Nick Higham (University of Manchester) advocated in his invited lecture using arithmetics of different precision at different stages of computations in order to design algorithms that are faster, require less communications and consume less energy. The main motivation is that last-generation GPUs may be up to eight times faster when they perform arithmetic operations in half precision than when they do in single precision.

The general philosophy is doing the bulk of the computations in half precision, and then perform some kind of clean-up refinement of the solution in higher precisions. As an archetypal example to illustrate this line of thought Higham chose how to accelerate the solution of linear systems via Gaussian elimination. He showed that if the LU factorization is computed in half precision, followed by iterative refinement using a mix of half, double and quadruple precision, the solution can be sped up significantly without accuracy loss. This works in principle for systems with moderate condition number, but even ill-conditioned systems can be dealt with by performing the iterative refinement via GMRES on a suitably pre-conditioned system.”

Photo credit Françoise Tisseur

Professor Françoise Tisseur delivered the Olga Taussky-Todd Lecture at the International Congress on Industrial and Applied Mathematics (ICIAM) on July 15, 2019, in Valencia, Spain. The honour of giving this lecture is conferred every four years on a woman who has made outstanding contributions in applied mathematics and/or scientific computation.

Her talk “Challenges in the numerical solution of nonlinear eigenvalue problems” (slides available here in PDF form) concerned eigenvalue problems defined in terms of matrix-valued functions of a scalar parameter, which occur in many areas of science and engineering. She described recent advances in numerical methods for solving such problems, which include methods for approximating by a rational or polynomial matrix function and methods for linearizing rational and polynomial eigenproblems. Pitfalls that the methods must overcome were illustrated through simple but realistic practical examples.

Her talk followed the opening ceremony, which included traditional Valencian dancing and an address to the approximately 4000 attendees by King Felipe VI of Spain (video clip), who spoke of the good health of Spanish mathematics and the importance of mathematics for driving innovation.