Special Guest Seminar: Nicholas Higham, The Rise of Multi-precision Computations

Guest Speaker: Nicholas J. Higham – School of Mathematics, University of Manchester (UK)

Biography Extract:
Nick Higham is Richardson Professor of Applied Mathematics in the School of Mathematics, University of Manchester. His degrees (BA 1982, MSc 1983, PhD 1985) are from the University of Manchester, and he has held visiting positions at Cornell University and the Institute for Mathematics and its Applications, University of Minnesota. He is Director of Research within the School of Mathematics, Head of the Numerical Analysis Group, and was Director of the Manchester Institute for Mathematical Sciences (MIMS) 2004-2010. He was elected Fellow of the Royal Society in 2007, and is a SIAM Fellow and a Member of Academia Europaea. He held a Royal Society-Wolfson Research Merit Award (2003-2008).

He is well known for his research on the accuracy and stability of numerical algorithms, and the second edition of his 700-page monograph on this topic was published by SIAM in 2002. His most recent book, Functions of Matrices: Theory and Computation (SIAM, 2008), is the first research monograph devoted to this topic. He is the Editor of the Princeton Companion to Applied Mathematics (2015, over 1000 pages).

Higham is a member of the editorial boards of the journals Acta Numerica, Forum of Mathematics, Foundations of Computational Mathematics. IMA Journal of Numerical Analysis, Linear Algebra and Its Applications, Numerical Algorithms, and Peer J Computer Science. He is also (Founding) Editor-in-Chief of the SIAM Fundamentals of Algorithms book series.

He is the current President of SIAM, and was Vice President at Large (2010-2013) and served for over ten years on the SIAM Board of Trustees and the SIAM Council. He has also served on the Board of Directors of the International Linear Algebra Society, and as Chair of the SIAM Activity Group on Linear Algebra. He is a frequent invited speaker at international conferences, served for 17 years on the (permanent) organizing committee of the Householder Symposia on Numerical Linear Algebra, and was a member of the Scientific Program Committee for ICIAM 2011…

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Talk Abstract

Multi-precision arithmetic means floating point arithmetic supporting multiple, possibly arbitrary, precisions. In recent years there has been a growing demand for and use of multi-precision arithmetic in order to deliver a result of the required accuracy at minimal cost. For a rapidly growing body of applications, double precision arithmetic is insufficient to provide results of the required accuracy. These applications include supernova simulations, electromagnetic scattering theory, and computational number theory. On the other hand, it has been argued that for climate modelling and deep learning half precision (about four significant decimal digits) We discuss a number of topics involving multi-precision arithmetic.

Lecture includes:

(i) How to derive linear algebra algorithms that will run in any precision, as opposed to be being optimized (as some key algorithms are) for double precision.

(ii) The need for, availability of, and ways to exploit, higher precision arithmetic (e.g., quadruple precision arithmetic).

(iii) What accuracy rounding error bounds can guarantee for large problems solved in low precision.

(iv) How a new form of preconditioned  iterative refinement can be used to solve very ill conditioned sparse linear systems to high accuracy.


No references provided at this time.

Supporting Media


26 Apr 2017, Nick Higham, “The Rise of Multiprecision Computations" from SAMSI on Vimeo.