Author Archives: Stephanie Lai

Massimiliano Fasi awarded PhD

Congratulations to Massimiliano Fasi for being awarded his PhD, which was supervised by Nick Higham. We asked him a few questions about his thesis, title Computing Matrix Functions in Arbitrary Precision Arithmetic.

Please can you introduce yourself and tell us a bit about your experience before attending University of Manchester?
I was born in Assisi, a smallish town in central Italy chiefly known for having been home to Saint Francis. I thought I would become a philologist, and during my teen years I studied mostly linguistics and ancient languages, while taking plenty of courses at the local music conservatory. After much pondering, I decided to start my university career with a scientific discipline and I chose computer science. I found that I really enjoyed the subject, and after graduating from the University of Perugia I pursued a Master’s degree at the University of Bologna and, at the same time, one at the École Normale Supérieure of Lyon.

What is your thesis on?
My thesis investigates the computation of matrix functions in arbitrary precision arithmetic, and is in fact a collection of results that are somewhat connected to this topic. We started by revisiting several well-known techniques for two very general problems: the evaluation of rational functions at a matrix argument and the solution of rational matrix equations. We developed new numerical methods and provided some theoretical insights, and used these as building blocks to design multiprecision algorithms to evaluate matrix functions that are of interest in applications. We focused mainly on the matrix exponential and the matrix logarithm, but the machinery we developed is more general and can be used for a much broader range of problems.

Why did you choose to study your PhD in Manchester?
Numerical analysis was my favourite module as an undergraduate student. I decided to do an internship with the lecturer teaching that course, and the subject happened to be the matrix Lambert W function. I’ve been interested in matrix functions ever since, and when the time came to choose where to do a PhD, I thought that it would be great to join the strongest linear algebra group I was aware of. I was lucky enough to be admitted at The University of Manchester, where I could do research with Professor Nick Higham, who is a leading expert in this field.

How did you find Manchester?
Manchester is a lively city and is well connected to the rest of the world. The postgraduate community I was part of is very dynamic, and somewhat larger than I was used to. A PhD can be rather difficult at times, but the many people I had the chance to meet here made my Mancunian experience unforgettable.

What’s your next step?
My long-term plan is to remain in academia, and I will try to follow the path that leads to a permanent position. For the moment, I am a research associate in the group here in Manchester, and am trying my best to deepen my understanding of the current trends in numerical linear algebra.


Massimiliano Fasi



Nick Higham awarded the LMS Naylor Prize and Lectureship

Professor Nick Higham has been awarded the London Mathematics Society’s Naylor Prize and Lectureship for his leadership in numerical linear algebra, numerical stability analysis, and communication of mathematics.

The Naylor Prize and Lectureship is awarded every two years in memory of Dr V. D. Naylor. The grounds for the award may include work in, and influence on, and contributions to applied mathematics and/or the applications of mathematics, and lecturing gifts.

The full prize citation is available here.

Higham, Nicholas FRS, 2015 DSC_3580 ed_cropped

Highlights of Advances in Numerical Linear Algebra Conference

by Sven Hammarling, Nick Higham and Françoise Tisseur

The conference Advances in Numerical Linear Algebra: Celebrating the Centenary of the Birth of James H. Wilkinson, took place at the University of Manchester, May 29-30, 2019.  The purpose of the conference was to discuss recent developments and future challenges in numerical linear algebra and to celebrate the centenary of the birth of James H. Wilkinson FRS (1919-1986).

The 60 attendees heard reminiscences about Wilkinson and his work from several attendees who knew him.  Sven Hammarling opened the proceedings with personal reflections on Wilkinson. Margaret Wright discussed some of the treasures in lecture notes from courses that Wilkinson taught at Stanford University (1977-1982). We have recently added these notes to our Wilkinson web page. Nick Higham announced the availability of the Argonne tapes, which are videos of Wilkinson and Cleve Moler lecturing at an Eigensystem Workshop held at Argonne National Laboratory, Illinois, USA, in June 1973.

We were pleased to welcome two of Jim Wilkinson’s nephews, John Liebman and Danny Liebman, together with John’s wife Liz.

Attendees were able to wish speaker Cleve Moler a happy 80th birthday and share two birthday cakes with him.

Photos from the conference appear below. Click on a photo to enlarge it.

Slides of the talks are available at the conference web page. The first day’s lectures were professionally videoed and the videos are available on the NLA group’s YouTube channel: here is a link to the playlist.

Thank you to all the speakers and attendees for their participation.

We gratefully acknowledge sponsorship from the Royal Society, The Alan Turing Institute, The QJMAM Fund for Applied Mathematics, The Numerical Algorithm Group and National Physical Laboratory.


Our Alumni – Pythagoras Papadimitriou

In this blog post, we asked one of our alumni, Pythagoras Papadimitriou, a few questions about his time with the Numerical Linear Algebra Group.
Pythagoras Papadimitriou

Please can you introduce yourself and tell us a bit about your experience before attending University of Manchester?

I was born in Athens and grew up there.  I studied Mathematics (B.Sc.) at Athens University. Then I did my national service and I moved to Manchester in September 1990 to attend the M.Sc. course “Numerical Analysis & Computing” at Manchester University.

What was your PhD thesis on?

The title of my Ph.D. is “Parallel Solution of SVD-Related Problems, with Applications”. The main part of my research dealt with the development of parallel algorithms for computing the Singular Value Decomposition and the Polar Decomposition. The algorithms were designed for the particular architecture of the KSR1, which was a virtual shared-memory parallel computer, a leading-edge parallel computer technology of the 90s.

Why did you choose to study your PhD in Manchester?

My initial plan was to complete my M.Sc. and work in industry. But when Nick Higham asked me to do a Ph.D. with him with a scholarship from S.E.R.C. I did not think twice. I am very proud that Nick was my supervisor.

How did you find Manchester?

It was an invaluable experience, three wonderful years. I made good friends and I am still in touch with most of them. When I left Manchester in October 1993 I took only good memories with me, including some of the best moments in my life. They say that Manchester has changed and the city is more beautiful now. I hope my sons will have the opportunity to study in Manchester.

Can you tell us about your career since leaving Manchester?

I joined the IT industry as a software engineer a few days after the submission of my Ph.D. thesis in October 1993. My first employer was a start-up in Greece. I joined Intrasoft SA, the then largest Systems Integrator in southeast Europe, in 1995. At Intrasoft SA, I moved from SW Development to Project Management in 1997 and to Sales in 1999. I joined Nortel Networks in Athens in January 2001 as Sales Director for Greece and Cyprus. A dream came true in October 2005 when I joined Sun Microsystems, a company that I admired from my Manchester days when I used Sun Unix workstations for carrying out my research. I headed the SW Business Unit of Sun Microsystems for 5 years, being responsible for a huge geography, from Saint Petersburg to Cape Town and from Vienna to Vladivostok! In January 2011 I joined HP in Athens as Managing Director. I moved to Vienna in September 2014 to join Oracle as Senior Sales Director responsible for Central Eastern Europe, Russia, Turkey and Central Asia. Today my organisation is responsible for the Systems partners of Oracle in this region plus in Italy, France and Iberia.

What is your current role?

I head the Systems Alliance and Channel organisation of Oracle for Italy, France, Iberia, Central Eastern Europe, Russia, Turkey and Central Asia. We are responsible for driving with our channel partners (Value Added Distributors, Value Added Resellers, Systems Integrators and Independent Software Vendors) the hardware business of Oracle in this region.

Françoise Tisseur elected as SIAM UKIE Section President

Professor Françoise Tisseur has been elected as the new SIAM United Kingdom and Republic of Ireland Section President (SIAM UKIE) for 2 years starting in May 2019.  She previously served as Vice President, 2013-2015.

In her candidate statement for the election, Françoise said “I would like to grow SIAM membership in our region. I will support the 14 SIAM student chapters, encourage the establishment of new ones, continue the recent SIAM-IMA cooperation and promote joint meetings between the two societies. I will work to ensure that the annual meeting is successful and has a suitably diverse program that includes industrial involvement.”

The SIAM UKIE Section was formed in 1996 by the Society for Industrial and Applied Mathematics (SIAM) with the aim of promoting and supporting applied and industrial mathematics in the UK and the Republic of Ireland.


Françoise Tisseur

Our Alumni – Ramaseshan Kannan

In this blog post, we asked one of our alumni, Ramaseshan Kannan, a few questions about his time with the Numerical Linear Algebra Group.

Ramaseshan Kannan SQ

Please can you introduce yourself and tell us a bit about your experience before attending University of Manchester?

I studied an Undergraduate and a Master’s in Civil and Structural Engineering at the Indian Institute of Technology in Chennai. Upon graduation I started working for Arup in India, developing finite element-based structural engineering software. In due course I became very interested in the “solver” stack of the code, which is the linear algebra layer. I asked if my employer would support my PhD in this area and, to my surprise, they agreed. However the funding I was being offered only covered a fraction of my tuition and expenses as I was a non-EU candidate. At this point the School of Maths and in particular my supervisors helped out and I was offered a school scholarship to do a collaborative PhD in the NLA group. That’s how I landed up in sunny Manchester.

What was your PhD thesis on?

I worked on a range of sparse linear algebra problems that originated in the software I was developing. The mainstay of my research was a new eigenvector clustering algorithm that allowed engineers to debug errors in their mathematical models. Other parts concerned the execution performance of matrix algorithms on parallel computers.

During the PhD I continued working for Arup as a technology translator implementing my own research back into commercial software. As a result I was able to see most parts of my PhD being used on real world problems, which was very satisfying.

Why did you choose to study your PhD in Manchester?

Having secured my employer’s funding we started scouting for research groups and centres of expertise around the world in the area of eigenvalue problems. Very soon it became clear that Manchester was a leader in both theory and numerical software so it was an obvious choice. In addition, my supervisors Nick Higham and Francoise Tisseur were open to making my rather bespoke arrangement work, all of which contributed to the decision.

How did you find Manchester?

I liked it so much that I haven’t left! I find it a great mix of practicality and opportunity. We have some of the best schools in the country. Plus we have the Peak District, the Lake District, and Yorkshire Dales all within a day-trip’s distance.

Can you tell us about your career since leaving Manchester?

After finishing my PhD I have continued to work for Arup in our Manchester office. Over the years I have been involved in a gamut of activities such as internal and external research including sponsored MSc and PhDs, writing numerical software, publishing and peer reviewing and consulting with engineers to understand their technical problems, to name a few.

What is your current role?

As above, I don multiple hats although my primary role is centred around developing numerical software with the eventual aim of making simulations faster, more accurate, or more productive for the end-user. I am also tasked with blue sky activities so, as an example, I’m looking at ways in which machine learning can be symbiotically used with traditional numerical analysis/engineering simulation to help engineers.

Jack Dongarra elected as Foreign Member of the Royal Society

Jack Dongarra

Professor Jack Dongarra

Jack Dongarra, Professor and Turing Fellow in the School of Mathematics and member of the Numerical Linear Algebra Group, has been elected as a Foreign Member of the Royal Society.  This honour recognizes his 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.

Dongarra’s software and libraries, which include LINPACK, EISPACK, LAPACK, the BLAS, MPI, ATLAS, PLASMA, MAGMA, and PAPI, are universally considered as standards, both in academia and industry. They excel in the accuracy of the underlying numerical algorithms and the reliability and performance of the software. They benefit a very wide range of users through their incorporation into software including MATLAB, Maple, Mathematica, Octave, R, SciPy, and vendor libraries.

The Royal Society is the oldest scientific academy in continuous existence, going back to 1663. Each year the Royal Society elects up to 52 new Fellows and up to 10 new Foreign Members. Fellows and Foreign Members are elected for life on the basis of excellence in science. Each candidate is considered on their merits and can be proposed from any sector of the scientific community.

The full list of the newly elected Fellows and Foreign Members of the Royal Society is available here.

Our Alumni – Sam Relton

In this blog post, we asked one of our alumni, Sam Relton, a few questions about his time with the Numerical Linear Algebra Group.


Please can you introduce yourself and tell us a bit about your experience before attending University of Manchester?

I was always pretty good at maths, because I liked understanding how things worked, and so I went to Manchester for my BSc. During that course I really enjoyed the numerical analysis and linear algebra modules because they underpin how all other mathematics is implemented in practice. I loved living in Manchester so I wanted to stick around, and I was lucky enough to be able to skip an MSc and go straight to a PhD in the NLA group.

What was your PhD thesis on?

My thesis was supervised by Nick Higham and called “Algorithms for Matrix Functions, their Frechet Derivatives, and Condition Numbers”. It consisted of four research papers covering theoretical and algorithmic advances in the computation of matrix functions, all woven together. Along with Nick, a few of these papers were co-authored with Awad Al-Mohy (a previous PhD student of Nick’s who was interested in similar problems).

Why did you choose to study your PhD in Manchester?

Manchester is a world-leading research group for numerical linear algebra and it was a privilege to learn from (and work with) the greatest researchers in the field. This also opens up a lot of opportunities in terms of attending conferences, visiting other institutions, and when looking for postdoctoral positions. Manchester is also a fantastic place to live, with plenty going on and a thriving community of PhD and post-doc researchers. I also had a few friends studying other courses that I shared a house with during my undergraduate degree and PhD.

How did you find Manchester?

I loved Manchester, it’s a large busy city full of interesting things to see and do whilst the cost of living is nowhere near that of London. Despite that, you can easily get into the countryside with a 30 minute drive! The maths department was brilliant with plenty of strong research groups to chat with, lots of seminars to attend, and a friendly and open atmosphere between all the staff and students.

Can you tell us about your career since leaving Manchester?

After doing a BSc, PhD, and 2 post-docs in high-performance computing at Manchester I decided to try something new. I now work in the School of Medicine at Leeds, applying complex statistical models and machine learning to electronic healthcare records (taken from GP and hospital databases) with collaborators in the School of Computing. Statistics and machine learning are really just a practical application of linear algebra / HPC, so much of what I learnt during my years in Manchester is still very relevant! Working with large interdisciplinary teams of doctors and nurses is an interesting change, and it’s nice to have direct impact on NHS policy decisions.

Version 4.0 of NLEVP Collection of Nonlinear Eigenvalue Problems

nlevpA new release, version 4.0, is available of the NLEVP MATLAB toolbox, which provides a collection of nonlinear eigenvalue problems. The toolbox has become a standard tool for testing algorithms for solving nonlinear eigenvalue problems.

When it was originally released in 2008, the toolbox contained 26 problems.  The new release contains 74 problems. It is now distributed via GitHub and is available at

Further details are given in An Updated Set of Nonlinear Eigenvalue Problems. The collection will grow and contributions are welcome.

The following table shows the 22 new problems in version 4.0 of the toolbox .4.0 NLEVP problems

Our Alumni – Edvin Hopkins

In this blog post, we asked one of our alumni, Edvin Hopkins, a few questions about his time with the Numerical Linear Algebra Group.

Craig Lucas

Please can you introduce yourself and tell us a bit about your experience before attending University of Manchester?

I obtained my BA in Mathematics from the University of Cambridge in 2005 and remained there for a few more years to do a PhD in numerical relativity. My association with the University of Manchester began in 2010, when I joined the NLA group as a KTP Associate, working on a joint project with NAG to implement some of the NLA group’s matrix function algorithms for the NAG Library.

Why did you choose to work with the University of Manchester?

The project I was involved in was a great opportunity to bridge the gap between academia and industry and to work with world leaders in their fields.

How did you find Manchester?

Well, I’m still there! It has really grown on me in the past few years, and is a great place to work.

Can you tell us about your careers since leaving Manchester?

At the end of the KTP project I continued in the NLA group as a post doctoral research associate, working with Professor Nick Higham for a year and half on his ERC-funded project on matrix functions. I then returned to work for NAG (in their Manchester office) which is where I am now. NAG still has very strong links with the University of Manchester and with the NLA group in particular.

What is your current role?

I am a Technical Consultant at NAG. My work involves implementing mathematical algorithms for the NAG Library, and high performance computing consultancy projects.

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