Year: 2018

Conference in Honour of Walter Gautschi

Last week I had the pleasure of attending and speaking at the Conference on Scientific Computing and Approximation (March 30-31, 2018) at Purdue University, held in honour of Walter Gautschi (Professor Emeritus of Computer Science and Mathematics at Purdue University) on the occasion of his 90th birthday.

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The conference was expertly organized by Alex Pothen and Jie Shen. The attendees, numbering around 70, included many of Walter’s friends and colleagues.

The speakers made many references to Walter’s research contributions, particularly in the area of orthogonal polynomials. In my talk, Matrix Functions and their Sensitivity, I emphasized Walter’s work on conditioning of Vandermonde matrices.

A Vandermonde matrix V_n is an n\times n matrix depending on parameters x_1,x_2,\ldots,x_n that has j th column [1, x_j, \ldots, x_j^{n-1}]^T. It is nonsingular when the x_i are distinct. This is a notoriously ill conditioned class of matrices. Walter said that he first experienced the ill conditioning when he computed Gaussian quadrature formulas from moments of a weight function.

Walter has written numerous papers on Vandermonde matrices that give much insight into their conditioning. Here is a very a brief selection of Walter’s results. For more, see my chapter Numerical Conditioning in Walter’s collected works.

In a 1962 paper he showed that

\displaystyle\|V_n^{-1}\|_{\infty} \le \max_i \prod_{j\ne i}\frac{ 1+|x_j| }{ |x_i-x_j| }.

In 1978 he obtained

\displaystyle\|V_n^{-1}\|_{\infty} \ge \max_i \prod_{j\ne i} \frac{ \max(1,|x_j|) }{ |x_i-x_j| },

which differs from the upper bound by at most a factor 2^{n-1}. A 1975 result is that for x_i equispaced on [0,1],

\displaystyle\kappa(V_n)_{\infty} \sim \frac{1}{\pi} e^{-\frac{\pi}{4}} (3.1)^n.

A 1988 paper returns to lower bounds, showing that for x_i \ge 0 and n\ge 2,

\displaystyle\kappa(V_n)_{\infty} > 2^{n-1}.

When some of the x_i coincide a confluent Vandermonde matrix can be defined, in which columns are “repeatedly differentiated”. Walter has obtained bounds for the confluent case, too.

These results quantify the extreme ill conditioning. I should note, though, that appropriate algorithms that exploit structure can nevertheless obtain accurate solutions to Vandermonde problems, as described in Chapter 22 of Accuracy and Stability of Numerical Algorithms.

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Ron DeVore speaking on Optimal Data Assimilation
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Photo of Nick Higham’s talk by David Gleich.

Palomino Blackwing Pencil Tribute to Ada Lovelace

Despite the deep penetration of digital tools into our lives, a lot of mathematics is still written by hand in pencil, and so it is appropriate that the Palomino Blackwing Volumes 16.2 pencil is a tribute to Ada Lovelace, the 19th century mathematician who worked on Charles Babbage’s proposed Analytical Engine.

The Palomino Blackwing, from California Cedar Products Company, is a modern version of the Blackwing pencil produced up until 1998 by the Eberhard Faber Pencil Company. The Blackwing was a favorite of luminaries such as John Steinbeck and Leonard Bernstein, and was much missed until CalCedar acquired the brand and started production of its own version of the pencil in 2011. Blackwing Volumes are limited editions “celebrating the people, places and events that have defined our creative culture”.

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The 16.2 in the volume name refers to the Analytical Engine’s storage capacity of 16.2 kB (enough to hold one thousand 40 decimal digit numbers). The matt white finish and matt black ferrule are “inspired by the simple styling of early personal computers”. The rear of the pencil contains a pattern that represents in binary the initials AAL that Lovelace used to sign her work.

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Blackwing pencils are available with four different graphite hardnesses, of which the 16.2 is the second firmest, roughly equivalent to a B, and the same as for the regular Blackwing 602. The following test compares the 16.2 with the Blackwing (no number, and the softest), the Dixon Ticonderoga HB, and the Staedtler Noris HB. The paper is Clairefontaine and the shaded area shows a smear test where I rubbed my thumb over the shaded rectangle.

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The pencils come in packs of 12 and are available at, for example Bureau Direct (UK), pencils.com (USA), and JetPens (USA). If you’re in New York City, pop into Caroline Weaver’s wonderful CW Pencil Enterprise store.

One review has suggested that a harder graphite (as in certain other limited editions) would be better for writing mathematics. For me the 16.2 core is fine, but I also enjoy using the softer Blackwing cores. For a mathematician, as for any writer, having to pause to sharpen a pencil is not necessarily a bad thing, especially as the shavings give off a wonderful odor of the California incense cedar from which the barrels are made.

Photo Highlights of 2017

Here are some of my favourite photos taken at events that I attended in 2017.

Atlanta (January)

This was the first time I have attended the Joint Mathematics Meetings, which were held in Atlanta, January 4-7, 2017. It was a huge conference with over 6000 attendees. A highlight for me was the launch of the third edition of MATLAB Guide on the SIAM booth, with the help of The MathWorks: 170106-1123-14-5528.jpg Elizabeth Greenspan and Bruce Bailey looked after the SIAM stand: 170105-2056-12_5438.jpg If you are interested in writing a book or SIAM, Elizabeth would love to hear from you!

The conference was held in the Marriott Marquis Hotel and the Hyatt Regency Hotel, both of which have impressive atriums. This photo is taken taken with a fish-eye lens, looking up into the Marriott Marquis Hotel’s atrium 170104-2015-50-5388.jpg (For more photos, see Fuji Fisheye Photography: XT-2 and Samyang 8mm).

Atlanta (March)

I was back in Atlanta for the SIAM Conference on Computational Science and Engineering, February 27-March 3, 2017. A highlight was a 70th birthday dinner celebration for Iain Duff, pictured here speaking at the Parallel Numerical Linear Algebra for Extreme Scale Systems minisymposium: 170228-1020-54-5783.jpg Here is Sarah Knepper of Intel speaking in the Batched Linear Algebra on Multi/Many-Core Architectures symposium (a report on which is given in the blog post by Sam Relton) 170227-1712-57_5700.jpg Torrential rain one night forced me to take shelter on the way back from dinner, allowing a moment to capture this image of Peach Tree Street. 170301-1945-22_6376.jpg

Washington (April)

The National Math Festival was held at the Walter E. Washington Convention Center in Washington DC on April 22, 2017: 170422-1537-57_6202.jpg I caught the March for Science on the same day: 170422-1917-01_6325.jpg 170422-1944-58_6455.jpg

Pittsburgh (July)

The SIAM Annual Meeting, held July 10-14, 2017 at the David Lawrence Convention Center in Pittsburgh, was very busy for me as SIAM president. Here is conference co-chair Des Higham speaking in the minisymposium “Advances in Mathematics of Large-Scale and Higher-Order Networks”: 170713-1033-16_7413.jpg Emily Shuckburgh gave the I.E. Block Community Lecture “From Flatland to Our Land: A Mathematician’s Journey through Our Changing Planet”: 170712-1821-50_7337.jpg The Princeton Companion to Applied Mathematics was on display on the Princeton University Press stand: 170710-1728-15_7289.jpg Here are Des and I on the Roberto Clemente bridge over the Allegheny River, the evening before the conference started: 170708-2121-33_7255.jpg

Numerical Linear Algebra Group 2017

The Manchester Numerical Linear Algebra Group (many of whom are in the October 2017 photo below) was involved in a variety of activities this year. This post summarizes what we got up to. Publications are not included here, but many of them can be found on MIMS EPrints under the category Numerical Analysis.

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Software

Together with Jack Dongarra’s team at the University of Tennessee the group is one of the two partners involved in the development of PLASMA: Parallel Linear Algebra Software for Multicore Architectures.

PhD students Weijian Zhang, Steven Elsworth and Jonathan Deakin released Etymo—a search engine for machine learning research and development.

We continue to make our research codes available, which is increasingly done on GitHub; see the repositories of Fasi, Higham, Relton, Sego, Tisseur, Zhang. We also put MATLAB software on MATLAB Central File Exchange and on our own web sites, e.g., the Rational Krylov Toolbox (RKToolbox).

PhD Students

New PhD students Gian Maria Negri Porzio and Thomas McSweeney joined the group in September 2017.

Postdoctoral Research Associates (PDRAs)

Sam Relton, who was working on the Parallel Numerical Linear Algebra for Extreme Scale Systems (NLAFET) project, left in June 2017 to take up a position at the University of Leeds. Negin Bagherpour joined NLAFET in March 2017, leaving in November 2017.

Srikara Pranesh joined the project in November 2017. Pierre Blanchard joined us in October 2017 to work jointly on the ICONIC project (which started in June 2017) and NLAFET.

Presentations at Conferences and Workshops

UK and Republic of Ireland Section of SIAM Annual Meeting, University of Strathclyde, January 12, 2017: Fasi, Gwynne, Higham, Zemaityte, Zhang.

2017 Joint Mathematics Meetings, Atlanta, January 4-7, 2017: Higham.

Workshop on Matrix Equations and Tensor Techniques, Pisa, Italy, February 13-14 2017: Fasi

Due Giorni di Algebra Lineare Numerica, Como, Italy, February 16-17, 2017: Fasi

International Conference on Domain Decomposition Methods DD24, Svalbard, Norway, February 6-10, 2017: Sistek.

Workshop on Batched, Reproducible, and Reduced Precision BLAS, Atlanta, February 23-25, 2017: Hammarling, Relton.

SIAM Conference on Computational Science and Engineering, Atlanta, February 27-March 3, 2017: Relton, Zounon. See the blog posts about the meeting by Nick Higham and Sam Relton.

High Performance Computing in Science and Engineering (HPCSE) 2017, Hotel Solan, Czech Republic, May 22-25, 2017: Sistek

Advances in Data Science, Manchester, May 15-16, 2017: Zhang.

27th Biennial Conference on Numerical Analysis, Glasgow, June 27-30, 2017: Tisseur.

Householder Symposium XX on Numerical Linear Algebra, The Inn at Virginia Tech, June 18-23, 2017: Tisseur.

SIAM Annual Meeting, Pittsburgh, July 10-14, 2017: Zhang (see this SIAM News article about Weijian’s presentation). A Storify of the conference is available in PDF form.

ILAS 2017 Conference, Iowa State University, USA, July 24-28, 2017: Güttel

24th IEEE Symposium on Computer Arithmetic, London, July 24-26, 2017: Higham (see this blog post by George Constantinides).

LMS-EPSRC Symposium on Model Order Reduction, Durham, UK, August 8-17, 2017: Güttel

Euro-Par 2017, 23rd International European Conference on Parallel and Distributed Computing, August 28-September 1, 2017: Zounon.

INdAM Meeting Structured Matrices in Numerical Linear Algebra: Analysis, Algorithms and Applications, Cortona, Italy, September 4-8, 2017: Fasi, Tisseur.

2017 Woudschoten Conferences, Zeist, The Netherlands, 4-6 October 2017: Tisseur.

ICERM Workshop on Recent Advances in Seismic Modeling and Inversion, Brown University, USA, November 6-10, 2017: Güttel. A video recording of this talk is available.

Conference and Workshop Organization

Güttel co-organized the SIAM UKIE Annual Meeting 2017 at the University of Strathclyde January 12, 2017 and the GAMM ANLA Workshop on High-Performance Computing at the University of Cologne, September 7-8, 2017.

The Manchester SIAM Student Chapter organized an Manchester Chapter Auto Trader Industry Problem Solving Event on February 22, 2017 and the 7th Manchester SIAM Student Chapter Conference on May 5, 2017.

The group organized three minisymposia at the SIAM Conference on Computational Science and Engineering, Atlanta, February 27-March 3, 2017:

Visitors

Franco Zivcovic (Università degli Studi di Trento) visited the group from September 2017-January 2018.

Knowledge Transfer

The Sabisu KTP project, which ended in December 2016, has been awarded the highest grade of “Outstanding” by the KTP Grading Panel. A new KTP project with Process Integration Ltd. is under way, led by Stefan Güttel.

The MSc project of Thomas McSweeney was sponsored by NAG and produced a code for modified Cholesky factorization that will appear in the NAG Library.

Recognition and Service

Stefan Güttel continued his terms as Secretary/Treasurer of the SIAM UKIE section and vice-chair of the GAMM Activity Group on Applied and Numerical Linear Algebra.

Nick Higham served the first year of his two-year term as President of SIAM.

Weijian Zhang was awarded a SIAM Student Travel Award to attend the SIAM Annual Meeting 2017 in Pittsburgh.

Massimiliano Fasi and Mante Zemaityte were selected to present posters at the SET for Britain 2017 competition, which took place at the House of Commons, London. Fasi’s poster was “Finding Communities in Large Signed Networks with the Weighted Geometric Mean of Laplacians” and Zemaityte’s was “A Shift-and-Invert Lanczos Algorithm for the Dynamic Analysis of Structures”.

Jakub Sistek served as treasurer of the eu-maths-in.cz Czech Network for Mathematics in Industry.

Tweets of the Year