Author Archives: Nick Higham

Numerical Linear Algebra Group Activities 2022

During 2022 the Numerical Linear Algebra Group introduced a new logo, designed by Massimiliano Fasi, former PhD student and Research Associate in the group.

We published interviews with alumni Younes Chahlaoui and Vanni Noferini.

In addition to our papers in journals we published articles in SIAM News:

and a book

The award of the ACM A. M. Turing Award to Jack Dongarra was a highlight.

PhD Students

Zhengbo Zhou started as a PhD student, working with Nick Higham and Françoise Tisseur.

Xiaobo Liu (Computing Matrix Functions in Arbitrary Precision Arithmetic) and Michael Connolly (Probabilistic Rounding Error Analysis for Numerical Linear Algebra) successfully defended their PhD dissertations. Michael is now working as a data scientist at Bet365.

Postdoctoral Research Associates (PDRAs)

Xiaobo Liu and Bastien Vieuble took up PDRA positions towards the end of the year to work with Nick Higham.

Mantas Mikaitis left the group to take up a lectureship in the School of Computing at the University of Leeds on September 1st. He joined us in 2019 to take up his EPSRC Doctoral Prize Fellowship and he was a PDRA in the group from 2020.

Presentations at Conferences and Workshops

International Congress of Mathematics (ICM), July 6–14, 2022: Higham, invited sectional talk Numerical Stability of Algorithms at Extreme Scale and Low Precisions (slides, video).

A Journey in Numerical Linear Algebra: A Workshop in Honor of Michele Benzi’s 60th Birthday, University of Pisa, June 10–11, 2022: Higham.

Linear Algebra, Matrix Analysis and Applications-ALAMA 2022-ALN2gg, Madrid, 1–3 June 2022: Tisseur.

Householder Symposium XXI on Numerical Linear Algebra, Selva di Fasano, Italy, 12–17 June 2022: Fasi, Tisseur.

Computational Mathematics for Quantum Technologies, Bath, August 1–5, 2022: Güttel.

7th IMA Conference on Numerical Linear Algebra and Optimization, University of Birmingham, June 29–July 1, 2022: Liu, McInnerney.

2022 SIAM Annual Meeting, July 11–15, 2022: Liu.

Conference and Workshop Organization

Sixteen members of the Group attended a two-day creativity Workshop held in April 2022, facilitated by Dennis Sherwood, an expert in creativity. See this report on the workshop.

Mantas Mikaitis and Nick Higham organized a double minisymposium Understanding and Exploiting Mixed-Precision Accelerators for High-Performance Computing at the SIAM Conference on Parallel Processing for Scientific Computing (PP22) in February 2022. Slides of some of the talks are available.

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, organized by Stefan Güttel, Sven Hammarling, Stephanie Lai, Françoise Tisseur and Marcus Webb. Most of the talks are available on the NLA Group YouTube channel and links to them are available on the conference web page. Photos are available here.

Recognition and Service

Jack Dongarra received the 2021 ACM A.M. Turing Award.

Nick Higham was elected Fellow of Royal Academy of Engineering.

Stefan Güttel was awarded the 2023 ILAS Taussky–Todd Prize.

Stefan Güttel was reappointed for another term as a member of the SIAM Membership Committee, 1/1/2023–12/31/2025.

Stefan Güttel Awarded 2023 ILAS Taussky-Todd Prize

Professor Stefan Güttel has been awarded the Taussky–Todd Prize by the International Linear Algebra Society (ILAS).

The ILAS Taussky-Todd Prize is given every three years at an ILAS Conference to an outstanding mid-career researcher in the field of linear algebra, for distinguished contributions to the field within about fifteen years of receiving the PhD or equivalent degree.

The 2023 ILAS Taussky–Todd Prize honours Professor Güttel’s “deep and impactful work on rational Krylov methods for nonlinear eigenvalue problems and matrix functions, in all aspects: analysis, software development, and applications”.

The prize is named for Olga Taussky and John Todd, who had a decisive impact on the development of theoretical and numerical linear algebra for over half a century. It honours them for their many and varied mathematical achievements and for their efforts in promoting linear algebra and matrix theory.

Professor Güttel will deliver a prize lecture at the 25th ILAS Conference in Madrid, 12 to 16 June 2023.

Nick Higham Elected Fellow of Royal Academy of Engineering

Congratulations to Professor Nick Higham, who has been
elected Fellow of Royal Academy of Engineering, in recognition for developing
“theory, algorithms and software that have had major impacts on
engineering practice in fields ranging from structural engineering to
financial modelling”.

The full citation is at https://raeng.org.uk/about-us/fellowship/new-fellows-2022/professor-nicholas-higham-freng-frs

Nick Higham

A Logo for the Numerical Linear Algebra Group

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The Numerical Linear Algebra Group recently held a competition amongst its members to design a logo for the group. Chosen from among four excellent entries, the winner was designed by Max Fasi, former PhD student and Research Associate in the group and now an external member of it.

The logo contains a matrix with a sparsity pattern that depicts a bee, the symbol of the city of Manchester since 1842. The bee symbolized the hard work of Mancunians during the industrial revolution.

You’ll see the logo on our slides and our social media accounts, and perhaps on physical items in due course.

Jack Dongarra Receives 2021 ACM A.M. Turing Award

Congratulations to Jack Dongarra who has received the 2021 ACM A.M. Turing Award. He is cited “for pioneering contributions to numerical algorithms and libraries that enabled high performance computational software to keep pace with exponential hardware improvements for over four decades.”

Dongarra has been Turing Fellow in the Department of Mathematics since 2007, and also holds appointments at the University of Tennessee and Oak Ridge National Laboratory.

In summer 2021 the NLA Group organized a workshop New Directions in Numerical Linear Algebra and High Performance Computing: Celebrating the 70th Birthday of Jack Dongarra. Videos of talks, including one by Dongarra, are available here and provide much insight into Dongarra’s career and achievements.

The photo below shows Dongarra speaking at the 2019 Manchester workshop Advances in Numerical Linear Algebra: Celebrating the Centenary of the Birth of James H. Wilkinson. Wilkinson, seen at the top eight-hand corner of the slide, won the Turing Award in 1971.

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Jack Dongarra

Françoise Tisseur Awarded the LMS Fröhlich Prize

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.

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Nick Higham Interviewed in The Actuary Magazine

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.

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Online Seminar Series on Numerical Linear Algebra

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.

Françoise Tisseur Delivers the Olga Taussky-Todd Lecture at the ICIAM Congress in Valencia

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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 F 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 F 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.

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The Contribution of Dr. J. H. Wilkinson to Numerical Analysis

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President HRH Duke of Edinburgh presenting honorary fellowship of The Institute of Mathematics and its Applications to James Wilkinson in 1977 (© The IMA).

The title of this post is the same as that of a symposium organized by Michael J. D. Powell and the Institute of Mathematics and its Applications (IMA) at the Royal Society in London on July 6th, 1977. The meeting commemorated the election of James Hardy Wilkinson to an Honorary Fellowship of the IMA.

The proceedings of the meeting were published by the IMA in a 91-page A5 booklet. As far as I am aware, few copies of the booklet survive and its contents have not previously been made available online. I am grateful to David Youdan, Executive Director of the IMA, for giving me permission to provide here a scan of the booklet. It is timely to do so, because this year marks the 100th anniversary of the birth of Wilkinson.

Here are the individual chapters, with comments from Mike Powell’s preface in quotes.

  • About Jim Wilkinson, with a Commemorative Snippet on Backward Error Analysis, L. Fox (Oxford University Computing Laboratory). “Leslie Fox describes many of Jim Wilkinson’s achievements that have not been published before and he exposes the accuracy of some ill-conditioned least squares calculations.”
  • Inverse Iteration, Newton’s Method, and Non-linear Eigenvalue Problems, M. R. Osborne (Australian National University). “Mike Osborne unifies the convergence properties of a main class of iterative methods for calculating eigenvalues.”
  • A New Look at Error Analysis, C. W. Clenshaw (University of Lancaster). “Charles Clenshaw develops an idea, due to Frank Olver, for treating the accumulation of errors in floating point arithmetic.”
  • A Problem in Numerical Linear Algebra, J. H. Wilkinson (National Physical Laboratory). “Jim Wilkinson shows the relevance in practice of the equivalence of repeated matrix eigenvalues, the ill-conditioning of the matrix eigenvector calculation, and the orthogonality of left and right hand eigenvectors that have a common eigenvalue.”

For more information about Wilkinson, see this web page that Sven Hammarling and I have created.

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