Remembering James Hardy Wilkinson
By Sven Hammarling and Nicholas Higham
James Hardy Wilkinson
The 5th of October 2016 is the 30th anniversary of the death of James Hardy Wilkinson, or Jim Wilkinson as he was affectionately known for much of his working life. Jim had a big influence on the careers of both authors and so we felt that it was appropriate to remind colleagues of the person that was Jim.
Jim obtained a B.A. in mathematics, with first class honours and distinction, at Cambridge University in 1939 at age 19. His tutors included G. H. Hardy, J. E. Littlewood and A. S. Besicovitch. In January, 1940 Jim was drafted into military scientific work for the Ministry of Supply, working in areas such as ballistics and the thermodynamics of explosions. It was during his time at Fort Halstead that he met his wife, Heather, also a graduate with a first class honours degree in mathematics and they lived happily together for forty years.
At the end of the war, Jim joined the Mathematics Division of the National Physical Laboratory (NPL), where he remained for the rest of his employment, although he continued working after his formal retirement until the time of his death (the rules of his post required him to retire at 60). It is fun to see the occasional paper for which the author’s address is 40 Atbara Road!
At NPL, Jim nominally worked half time for Alan Turing and half time for the Desk Computing Section, although in practice he spent most of his time with Turing working on the Automatic Computing Engine (ACE), a computer designed by Turing. Jim became lifelong friends with Leslie Fox, who also worked for The Desk Computing Section. Leslie later established the Oxford University Computing Laboratory and wrote the Royal Society Biographical Memoir on Jim [2]. When Turing left on sabbatical leave in 1947 and then permanently for the University of Manchester in 1948, Jim was left in charge of the ACE Section. Pilot ACE first worked in May 1950 and was successfully demonstrated to the press in November 1950. A cartoon about Pilot ACE even appeared in the Daily Mirror! See page 103 of [1]. Turing told Jim how much better they had done than would have been possible had he stayed.
Once Pilot ACE started working, Jim began using it to solve problems, particularly in numerical linear algebra. He had at that time an almost unique knowledge of hardware, software and mathematics, particularly numerical analysis. Jim always said that his hands-on experience solving problems with desk calculators and Pilot ACE was fundamental to his understanding of numerical algorithms.
As readers will be well aware, Jim went on to develop the theory and practice of backward error analysis, particularly in the context of numerical linear algebra, and to produce detailed analyses of algorithms and software implementing those algorithms (see [2], [3] and [4]). He has left us a lasting and important legacy.
Jim was the first numerical analyst of the modern era to be elected, in 1969, a Fellow of the Royal Society. Of his many honours, it is notable that he received both the ACM Turing and the SIAM Von Neumann awards in the same year, 1970. To date, that is unique.
Following Jim’s death, a conference was held in his honour, the proceedings of which are available in [6]. The papers bear reading to this day and make a very fitting tribute to Jim. At the conference, there were many comments on Jim’s influence, both of his personal friendship and support, and of his technical influence. The establishment of the Wilkinson Prize for Numerical Software was announced at the end of the conference, to be supported by Argonne National Laboratory, NAG Ltd and NPL, all of which had strong connections with Jim. In 2015, SIAM kindly agreed to take on the administration of the prize, thereby helping to ensure its future. The James H. Wilkinson Prize in Numerical Analysis and Scientific Computing had already been established by SIAM in 1979, appropriately intended to stimulate the careers of younger scientists, so, uniquely, Jim now has two SIAM prizes in his honour. Argonne National Laboratory created a Wilkinson Fellowship in Scientific Computing, again intended for younger workers in the field.
Both of us were strongly influenced in our careers by Jim. SH was lucky enough to spend a sabbatical year with Jim at NPL and that undoubtedly had a profound effect on his future. NJH has been strongly influenced by Wilkinson’s work on rounding error analysis, which remains today as powerful, elegant and readable as when it was first written.
We have recently set up a Google Scholar page for Jim. The Algebraic Eigenvalue Problem alone has nearly 10,000 citations. Many photos related to Jim, mostly supplied by Heather, can be found here.
We are aware of at least three audio interviews concerning Jim. One is by John Nash and a transcript is available at SIAM’s oral history website. The second is in the Pioneers of Computing series of interviews compiled by Christopher Evans, with the support of the Science Museum, London, and NPL. The third is a 1982 NPL video, available on YouTube, in which Mike Woodger—who also worked with Alan Turing—and Jim discuss Pilot ACE and Alan Turing. Gene Golub closed his contribution to the memorial conference proceedings by saying:
Jim Wilkinson was an extraordinary scientist who created and developed a field. I think of myself as someone who applies the principles that were handed down by him in a variety of applications. The numerical linear algebra community was fortunate to have the inspiration of this great and good man. Not only did he provide scientific leadership but he was a wonderful man of unusual warmth, wit and kindness. I miss him greatly.
Let us not forget James Hardy Wilkinson.
[2] L. Fox. James Hardy Wilkinson. In Biographical Memoirs of Fellows of the Royal Society, Volume 33, pages 671708. The Royal Society, London, UK, 1987.
[3] J. H. Wilkinson. Rounding Errors in Algebraic Processes. Notes on Applied Science, No.32. HMSO, London, UK, 1963. (Also published by Prentice-Hall, Englewood Cliffs, NJ, USA, 1964, translated into Polish as Bledy Zaokraglen w Procesach Algebraicznych by PWW, Warsaw, Poland, 1967 and translated into German as Rundungsfehler by Springer-Verlag, Berlin, Germany, 1969. Reprinted by Dover Publications, New York, 1994).
[4] J. H. Wilkinson. The Algebraic Eigenvalue Problem. Oxford University Press, Oxford, UK, 1965. (Also translated into Russian by Nauka, Russian Academy of Sciences, 1970).
[5] J. H. Wilkinson and C. Reinsch, editors. Handbook for Automatic Computation, Volume II, Linear Algebra. Springer-Verlag, Berlin, Germany, 1971.
[6] M. G. Cox and S. Hammarling, editors. Reliable Numerical Computation. Oxford University Press, Oxford, UK, 1990.