Conference Report

The IMA Conference on Linear Algebra and Its Applications was held at Hulme Hall, University of Manchester, from 9th-12th July 1995. The meeting, which was the first major linear algebra conference to be held in the U.K. for seven years, drew a truly international audience with 111 participants from 21 different countries in 5 continents. The organising committee of Nick Higham (Manchester), Iain Duff (Rutherford Appleton Laboratory and CERFACS), Roger Fletcher (Dundee), Len Freeman (Manchester), Sven Hammarling (NAG Ltd., Oxford) and Nancy Nichols (Reading) had done an excellent job of assembling a varied and interesting programme to attract people from many areas of linear algebra.

Those visiting Manchester for the first time were particularly impressed by the glorious sunshine which prevailed for the Wine Reception provided by the University on Sunday evening and for the following day. Official proceedings were opened on Monday morning by the Chair of the organising committee, Nick Higham, whose welcoming speech included a reminder of some of the city's rich history of scientific discovery. Two and a half days of plenary invited talks, interspersed with invited and submitted talks in two or three parallel sessions, were then kicked off by Gene Golub (Stanford) who spoke on `Large-scale matrix computation problems from Quantum Chromodynamics'. The international mix of participants was reflected in the choice of plenary invited speakers, with an American morning of Margaret Wright (AT&T Bell Labs) discussing `Something old, something new, something borrowed: connections between linear algebra and optimization' and Richard Brualdi (Madison) on `Spectral radius of matrices of zeros and ones' followed by a European afternoon: Per Christian Hansen (UNI.C, Denmark) considered `Regularization of large-scale discrete ill-posed problems' and Henk van der Vorst (Utrecht) described `A generalized Jacobi-Davidson iteration for linear eigenvalue problems'.

The Monday evening session was a poster one, with 27 contributions on display. The organising committee had expressed a strong belief that posters are an increasingly important mode of presentation and Nick Higham and Sven Hammarling had written a short article on `How To Prepare A Poster' which was available before the meeting. The result was a splendid selection of posters prepared to a high standard. To encourage debate on what makes a good poster, there were also prizes available for the best presentations as judged by a panel headed by Sven Hammarling.

The parallel sessions on Tuesday morning were sandwiched between two more excellent invited plenary presentations: `Recent progress in serial and parallel algorithms for the algebraic eigenvalue problem and SVD' given by Jim Demmel (Berkeley), and a discussion by Roger Horn (Utah) of `Hadamard products, unitarily invariant norms and perturbation bounds for the polar decomposition'. One other stipulation of the organising committee had been their desire to promote `lively discussion' and questioning after talks, so those chairing the sessions were encouraged to adopt a Draconian approach to time-keeping. The timetable clearly allocated 5 minutes for questions after each talk and speakers were specifically asked not to run into this period. This strategy seemed to work very well throughout, despite certain clock discrepancies between rooms which led Iain Duff to suggest synchronising watches to `Hulme Hall Mean Time' for the duration of the meeting.

Tuesday afternoon was set aside as free time, with a number of possible excursions on offer including a visit to the Manchester Museum of Science and Industry, Granada Studios or the Castlefield Roman Fort. Unfortunately the good weather chose this time to break in somewhat spectacular fashion, but the major thunderstorms and ensuing torrential rain did not seem to dampen the general enthusiasm. The evening began with a sherry reception sponsored by Mathworks in the impressive surroundings of Manchester Town Hall, followed by the conference dinner. Nick Trefethen (Cornell) gave a lively and entertaining after-dinner speech, concluding with an epic poem crafted out of the titles of every talk and poster presented at the conference (see below).

The winners of the poster prizes were also revealed at the dinner, with Sven Hammarling announcing the names and Margaret Wright, President of SIAM, presenting the prizes. A copy of Matlab went to overall winner Bruno Lang (Wuppertal) for his colourful presentation of `Using Level~3 BLAS in the $QR$ and $QL$ Algorithms', with Erik Elmroth (Umea) winning a copy of the student version of Mathematica for his display on `A Versal Deformation Approach to Perturbation Theory of Matrices and Matrix Pencils' (best poster by a graduate student). There were also `honourable mentions' (and a choice of books from those on display) for Peter Benner (Chemnitz--Zwickau), Fabio Guerinoni (IRISA/INRIA), Harvinder Jhass (Bristol) and Kim-Chuan Toh (Cornell) for their efforts.

On Wednesday morning, the difficult task of following the conference dinner was consummately performed by Andy Wathen with his talk on `Iterative solution of large sparse and indefinite linear systems arising in PDEs'. There followed more parallel sessions, topped off before lunch by Paul van Dooren's discussion of `The Schur algorithm for Toeplitz matrices'. The final plenary session of the week was a presentation on `Teaching the Applications' by Gil Strang, complete with exercises and homework for the audience. A last set of parallel contributed talks rounded off the day and the conference.

Photographs from the conference, including shots of the winning posters, are available from the conference Web page, which has the URL (uniform resource locator) http://www.ma.man.ac.uk/MCCM/laa95.html. Thanks are due to the organising committee for a most enjoyable conference, and hopefully it will not be another seven years until we see another major linear algebra meeting in the UK.

Alison Ramage
Lecturer, Department of Mathematics
University of Strathclyde, Glasgow

A SCHUR METHOD FOR SHARPENING LARGE MATRIX PENCILS
by L. N. Trefethen

Are you feeling sparse and of ill condition?
Have you got the Level 3 BLAS?
Constrained to a nullspace? Ill-posed? Non-hermitian?
Not half the man you was?

Are you unstructured and backward-unstable?
A jumble of zeros and ones?
Blown out of your disk by the least perturbation?
Defective? Nilpotent? All thumbs?

Then don't be a block matrix! Don't let them say UMIST
Lanczos and Chebyshev, Wiener and Hopf,
Vandermonde, Toeplitz, Jacobi and Davidson,
Cayley, Laplace, Helmholtz, Gauss and Krylopf!

For I've something new to restore your blurred image
To return you forthwith to canonical form
A totally positive robust realization
Guaranteed to achieve your invariant norm.

Precondition yourself up to sunny Manchester!
Join our dense family of 1 x 2 blocks!
Our eigenvalues are some of the best---or
Better still, check out our pseudospec talks!

Spatially variant, massively parallel,
Centro-symmetric---yes, we've got it all.
Hadamard products, quadruples of matrices,
Fourth-order tensors---just come to Hulme Hall!

To blend in among us, just mutter convincedly
QR, QL, QCD, KKT,
$n \log n$, $J'$, $J'_\nu$ and GMRES
SVD, LU, $\ell^2$ and $\ell^p$!

We'll regularize you and we'll do it cubically,
We'll update your focus and style and pace.
Our primal-dual methods will square your determinant
And that's not the half what we'll do to your trace!

At the end of the week, when it's time for deflation,
Order a Guinness of maximum rank
Invert it directly but keep it controllable
And offer a toast up to those we must thank:

[Versal deformation:]

To the woman whose organisational featles
Do the IMA proud, Mrs Pamela Bye-am!
And to north England's finest export since the Beatles,
Our polymathematician, Nicholas Higham!