This year’s group photo was taken on March 5, 2020 after the NLA group meeting. Most group members are in the photo; those missing include Jack Dongarra,Stefan Güttel, Ramaseshan Kannan and Marcus Webb.
The banner on this website has also been updated with the new group photo. A high resolution version of the photo is available here.
By row from the back: Craig Lucas, Nick Higham, Xinye Chen, Steven Elsworth, Xiaobo (Bob) Liu, Michael Connolly, Mantas Mikaitis, Len Freeman, Massimiliano Fasi, Pierre Blanchard, Sven Hammarling, Asad Raza Aitor Mehasi Mehasi, Stephanie Lai, Gian Maria Negri Porzio, Thomas McSweeney Mawussi Zounon, Françoise Tisseur, Srikara Pranesh, Yuqing (Mila) Zhang, Eleni Vlachopoulou.
Most backward error bounds for numerical linear algebra algorithms are of the form , for a machine precision and a problem size . The dependence on of these bounds is known to be pessimistic: together with Nick Higham, our recent probabilistic analysis [SIAM J. Sci. Comput., 41 (2019), pp. A2815–A2835], which assumes rounding errors to be independent random variables of mean zero, proves that can be replaced by a small multiple of with high probability. However, even these smaller bounds can still be pessimistic, as the figure below illustrates.
The figure plots the backward error for summation (in single precision) of floating-point numbers randomly sampled from a uniform distribution. For numbers in the distribution, the bound is almost sharp and accurately predicts the error growth. However, for the distribution, the error is much smaller, seemingly not growing with . This strong dependence of the backward error on the data cannot be explained by the existing bounds, which do not depend on the values of the data.
In our recent preprint, we perform a new probabilistic analysis that combines a probabilistic model of the rounding errors with a second probabilistic model of the data. Our analysis reveals a strong dependence of the backward error on the mean of the data : indeed, our new backward error bounds are proportional to . Therefore, for data with small or zero mean, these new bounds are much sharper as they bound the backward error by a small multiple of the machine precision independent of the problem size .
Motivated by this observation, we also propose new algorithms that transform the data to have zero mean, so as to benefit from these more favorable bounds. We implement this idea for matrix multiplication and show that our new algorithm can produce significantly more accurate results than standard matrix multiplication.
Professors Jack Dongarra and Nick Higham, together with Dr Laura Grigori (Inria Paris), have edited the issue Numerical Algorithms for High-Performance Computational Science of the journal Philosophical Transaction of The Royal Society A. The issue is now available online.
The issue contains papers from a Discussion meeting of the same title organized at the Royal Society in April 2019. A report on that meeting, along with photos from it, is available here. The content of the issue, with links to the papers, is as follows.
Professor Jack Dongarra, a member of the Manchester Numerical Linear Algebra Group who also holds appointments at the University of Tennessee and Oak Ridge National Laboratory, has been named as recipient of the IEEE Computer Society’s 2020 Computer Pioneer Award.
The award is given for significant contributions to early concepts and developments in the electronic computer field that have clearly advanced the state-of-the-art in computing. Dongarra is being recognized “for leadership in the area of high-performance mathematical software.”
Dongarra will receive his award at the Computer Society’s annual awards dinner and presentation to be held on Wednesday 27 May 2020 at the Hilton McLean Tysons Corner during the IEEE Computer Society Board of Governors meeting. The award consists of a silver medal and an invitation to speak at the award presentation.
Several members of the group attended the SIAM UKIE Section Meeting held at the University of Edinburgh on Friday January 10, 2020. Françoise Tisseur, President of the Section and one of the co-organizers, chaired the morning session.