J. H. Wilkinson's work and influence on matrix computations

Abstract

1. An Outline of His Career James Hardy Wilkinson died suddenly at his London home on October 5, 1986, at the age of 67. Here is a very brief account of his professional life. He won an open competition scholarship in mathematics to Trinity College, Cambridge, when he was 16 years old. He won two coveted prizes (the Pemberton and the Mathieson) while he was an undergraduate at Trinity College and graduated with first class honors before he was 20 years old. He worked aa a mathematician for the Ministry of Supply throughout World War II and it was there that he met and married his wife Heather. In 1947 he joined the recently formed group of numerical analysts at the National Physical Laboratory in Bushy Park on the outskirts of London. He was to stay there until his retirement in 1980. Soon after his arrival he began to work with Alan Turing on the design of a digital computer. That work led to the pilot (prototype) machine ACE which executed its first scientific calculations in 1953. Wilkinson designed the multiplication unit for ACE and its successor DEUCE. One could say that the decade 1947-1957 was the exciting learning period in which Wilkinson, and his colleagues at NPL, discovered how automatic computation differed from human computation assisted by desk top calculating machines. By dint of trying every method that they could think of and watching the progress of their computations on punched cards, paper tape, or even lights on the control console, these pioneers won an invaluable practical understanding of how algorithms behave when implemented on computers. Some algorithms that are guaranteed to deliver the solution after a fixed number of primitive arithmetic operations IN EXACT ARITHMETIC can produce, on some problems, completely wrong yet plausible output on a digital computer. That is the fundamental challenge of the branch of numerical analysis that Wilkinson helped to develop. 'The author gratefully acknowledges partial support from Office of Naval Research Contract ONR N00014-85-K-0180. The period 1958-1973 saw the development, articulation, and dissemination of this understanding of dense matrix computations. It was in 1958 that Wilkinson began giving short courses at the University of Michigan Summer College of Engineering. The notes served as the preliminary versions of his first two books. The lectures themselves introduced his work to an audience broader than the small group of specialists who had been brought together in …