History of Numerical Analysis

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William M. Kahan

Oral History (pdf)

Interviewer: Thomas Haigh

William Kahan discusses the whole of his career to date, with particular reference to his involvement with numerical software and hardware design. Kahan was born in Canada in 1933, growing up around Toronto. Kahan earned a B.A. in mathematics from the University of Toronto in 1954. He discusses in detail his experiences with the FERUT computer from 1953 onward, including its operation and use and the roles of Kelly Gotlieb, Beatrice Worsley, Cecily Popplewell, Joe Kates, and others. Kahan then began work on a Ph.D. from Toronto, graduating in 1958 under the direction of Byron A. Griffith. He outlines his thesis work on successive overrelaxation and his interest in backward error analysis. Kahan spent the summer of 1957 at the University of Illinois, where he used the ILLIAC and met Dave Muller, Don Gillies and Gene Golub. After graduation he spent two years in Cambridge, and he recounts his experiences using EDSAC II and interacting with Maurice Wilkes, Jim Wilkinson, Chris Strachey, Alan Curtis, and J.C.P. Miller. From 1960 to 1968, Kahan served as a faculty member at Toronto. He discusses his work with the IBM 7094, including efforts to rework its compiler, operating system, and elementary transcendental function library. Kahan also explores his role as part of the IBM SHARE user group to review the mathematical routines in its library and critique IBM’s early SSP package. Since 1968, Kahan has been on the faculty of the University of California, Berkeley. He recounts some of the history of its computer science department, and discusses his approach to teaching. Together with his students he produced the widely used fdlibm mathematics library. He explains the origins of some of his best known work, including the Kahan summation algorithm to correct for rounding errors, and a program he developed to test floating point arithmetic for errors.

Kahan offers an explanation of his work as a consultant. He designed the arithmetic for Intel’s i432 and 8087 chips. In 1989, Kahan won the ACM’s Turing Award, for his work in creating the IEEE 754 standard for floating-point computation during the late 1970s and early 1980s. He places this work in context, linking it both to his earlier experiences and to the proliferation of microprocessor designs during the 1970s. Kahan has also received the IEEE’s Emanuel R. Piore award and has been SIAM’s John von Neumann lecturer.

Key words: FERUT computer, ILLIAC, EDSAC II, IBM 7094, SHARE group, SSP, fdlibm math library, numerical algorithms, backward error analysis, floating point computation, IEEE 754 standard

Time frame: 1950's, 1960's, 1970's, 1980's

People: Byron A. Griffith, Gene Golub, Maurice Wilkes, Jim Wilkinson, Chris Strachey, Alan Curtis, J.C.P. Miller, Hirondo Kuki, Len Harding, James Demmel, Peter Tang, Brian T. Smith

Location: University of Toronto, Cambridge University, University of Illinois, University of California-Berkeley

Citation: William Kahan Oral history interview by Thomas Haigh, 5 - 8 August, 2005, Berkeley, California.  Society for Industrial and Applied Mathematics, Philadelphia, PA


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