The conference Advances in Numerical Linear Algebra: Celebrating the 60th Birthday of Nick Higham was held at the University of Manchester, July 6–8, 2022.

Most of the talks are available on the NLA Group YouTube channel and links to them are available on the conference web page.

Here is the conference photo.

(Hires version)

Here is me with some of my current and former PhD students.

(Hires version)

And with some of my current and former postdocs.

(Hires version)

After-dinner speaker Charlie Van Loan:

Rob Corless kindly gave me a Bohemian matrix eigenvalue tie based on this image.

Many thanks to Stefan Güttel, Sven Hammarling, Stephanie Lai, Françoise Tisseur and Marcus Webb for organizing the conference and the Royal Society, MathWorks and the University of Manchester for financial support.

In July 2021, Sven Hammarling, Françoise Tisseur and I organized an online workshop New Directions in Numerical Linear Algebra and High Performance Computing. The workshop brought together researchers working in numerical linear algebra and high performance computing to discuss current developments and challenges in the light of evolving computer hardware. It was held to honour Jack Dongarra on the occasion of his 70th birthday. The workshop had been postponed from July 2020 as a result of the pandemic.

Videos of the talks are now available on the Numerical Linear Algebra Group’s YouTube channel and are included below. Slides for the talks are available on the workshop website.

Sven Hammarling (The University of Manchester), “Jack Dongarra”.

Iain Duff (STFC-RAL and CERFACS), “Jack”

James Demmel (University of California, Berkeley), “New Communication-Avoiding Algorithms, and Fixing Old Bugs in the BLAS and LAPACK”

Piotr Luszczek (University of Tennessee), “Numerical Methods and Across Scales, Precisions and Hardware Platforms”

Cleve Moler (MathWorks), “Computers That I Have Known”

Yves Robert (Ecole Normale Supérieure de Lyon), “25+ Years of Scheduling at ICL”

Françoise Tisseur (The University of Manchester), “Mixed Precision Tall and Thin QR Factorization with Applications”

David Keyes (King Abdullah University of Science and Technology), “Adaptive Nonlinear Preconditioning for PDEs with Error Bounds on Output Functionals”

Zhaojun Bai (University of California, Davis), “Many Eigenpair Computation Via Hotelling’S Deflation”,

Ilse Ipsen (North Carolina State University), “A Few Observations About Summation Algorithms”

Erich Strohmaier (TOP500), “TOP500 and Accidental Benchmarking”

Nick Higham (The University of Manchester), “Solving Dense Linear Systems: A Brief History and Future Directions ”

Jack Dongarra (University of Tennessee, Oak Ridge Laboratory and The University of Manchester), “Still Having Fun After 50 Years”,

This minisymposium took place at the SIAM Conference on Computational Science and Engineering, March 2, 2021. This page makes available slides from some of the talks.

Minisymposium description: Reduced precision floating-point arithmetic, such as IEEE half precision and bfloat16, is increasingly available in hardware. Low precision computations promise major increases in speed and reductions in data communication costs, but they also bring an increased risk of overflow, underflow, and loss of accuracy. One way to improve the results of low precision computations is to use stochastic rounding instead of round to nearest, and this is proving popular in machine learning. This minisymposium will discuss recent advances in exploitation and analysis of reduced precision arithmetic and stochastic rounding.

Algorithms for Stochastically Rounded Elementary Arithmetic Operations in IEEE 754 Floating-Point Arithmetic Massimiliano Fasi, Örebro University, Sweden; Mantas Mikaitis, University of Manchester, United Kingdom. Abstract. Slides.

Reduced Precision Elementary Functions Jean-Michel Muller, ENS Lyon, France. Abstract. Slides.

Effect of Reduced Precision and Stochastic Rounding in the Numerical Solution of Parabolic Equations Matteo Croci and Michael B. Giles, University of Oxford, United Kingdom. Abstract. Slides.

Stochastic Rounding and its Probabilistic Backward Error Analysis Michael P. Connolly and Nicholas J. Higham, University of Manchester, United Kingdom; Theo Mary, Sorbonne Universités and CNRS, France. Abstract. Slides.

Stochastic Rounding in Weather and Climate Models Milan Kloewer, Edmund Paxton, and Matthew Chantry, University of Oxford, United Kingdom Abstract. Slides.

The Royal Society discussion meeting Numerical Algorithms for High-Performance Computational Science, which I organized with Jack Dongarra and Laura Grigori, was held in London, April 8-9, 2019. The meeting had 16 invited speakers and 23 contributed posters, with a poster blitz preceding the lively poster session.

The meeting brought together around 150 people who develop and implement numerical algorithms and software libraries—numerical analysts, computer scientists, and high-performance computing researchers—with those who use them in some of today’s most challenging applications. The aim was to discuss the challenges brought about by evolving computer architectures and the characteristics and requirements of applications, both to produce greater awareness of algorithms that are currently available or under development and to steer research on future algorithms.

Several key themes emerged across multiple talks, all in the context of today’s high performance computing landscape in which processor clock speeds have stagnated (with the end of Moore’s law) and exascale machine are just two or three years away.

• An important way of accelerating computations is through the use of low precision floating-point arithmetic—in particular by exploiting a hierarchy of precisions.
• We must exploit low rank matrix structure where it exists, for example in hierarchical (H-matrix) form, combining it with randomized approximations.
• Minimizing data movement (communication) is crucial, because of its increasing costs relative to the costs of floating-point arithmetic.
• Co-design (the collaborative and concurrent development of hardware, software, and numerical algorithms, with knowledge of applications) is increasingly important for numerical computing.

Applications treated included deep learning, climate modeling, computational biology, and the Square Kilometre Array (SKA) radio telescope project. We learned that the latter project needs faster FFTs in order to deal with the petabytes of data it will generate each year.

Papers from the meeting will be published in a future issue of Philosophical Transactions of the Royal Society A.

Here are the talks (in order of presentation), with links to the slides.

• Hierarchical algorithms on hierarchical architectures, David E. Keyes
• Antisocial parallelism: avoiding, hiding and managing communication, Katherine Yelick
• Big telescope, big data: towards exa-scale with the SKA, Anna Scaife
• Algorithms for in situ data analytics in next generation molecular dynamics workflows, Michela Taufer
• Numerical computing challenges for large-scale deep learning, Rick Stevens
• High-performance sampling of determinantal point processes, Jack Poulson
• Computing beyond the end of Moore’s Law, John Shalf
• Exascale applications: skin in the game, Douglas B. Kothe
• Machine learning and big scientific data, Tony Hey
• Iterative linear algebra in the exascale era, Erin Carson
• Stochastic rounding and reduced-precision fixed-point arithmetic for solving neural ODEs, Steve Furber
• Rethinking deep learning: architectures and algorithms, George Constantinides
• Reduced numerical precision and imprecise computing for ultra-accurate next-generation weather and climate models, Tim Palmer
• Memory-aware algorithms for automatic differentiation and backpropagation, Guillaume Aupy
• Post-K: the first ‘exascale’ supercomputer for convergence of HPC and big data/AI, Satoshi Matsuoka
• Accelerated sparse linear algebra: emerging challenges and capabilities for numerical algorithms and software, Michael A. Heroux

For a brief summary of the talks see George Constantinides’s insightful thoughts on the meeting.

Great turnout for @royalsociety discussion meeting. Kicking off with @nhigham introducing. pic.twitter.com/lNeQld2RN7

— G A Constantinides (@gconstantinides) April 8, 2019

Here are some photos from the meeting.

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