# William M. Kahan

### Research Areas

- Computer Architecture & Engineering (ARC)
- Scientific Computing (SCI)
- Computer architecture; Scientific computing; Numerical analysis

## Biography

William "Velvel" Kahan was born in Canada and attended the University of Toronto for both his undergraduate and graduate studies in mathematics, and was eventually hired there as a professor. He joined the Berkeley faculty in 1968 with a joint appointment in the Math Department and as a member of the new Computer Science Department in the College of Letters and Science--before it merged with the EECS Department in the College of Engineering in 1973. He retired from the University in 2008. Kahan was instrumental in creating the IEEE 754-1985 standard for floating-point computation in the late 1970s and early 1980s. He developed a program called "paranoia' in the 1980s to test for potential floating point bugs and developed the Kaham summation algorithm which helps minimize errors introduced when adding a sequences of finite precision floating point numbers. Kahan won the ACM A.M. Turing Award in 1989.

## Education

- 1958, Ph.D., Mathematics, University of Toronto
- 1956, Master's, Mathematics, University of Toronto
- 1954, B.A., Mathematics, University of Toronto

## Selected Publications

- W. M. Kahan, "Is there a small skew Cayley transform with zero diagonal?," Linear Algebra and Its Applications, vol. 417, no. 2-3, pp. 335-341, Sep. 2006.
- R. Bhatia, W. M. Kahan, and R. Li, "Pinchings and norms of scaled triangular matrices," Linear and Multilinear Algebra, vol. 50, no. 1, pp. 15-21, March 2002.
- W. M. Kahan and R. Li, "Unconventional schemes for a class of ordinary differential equations - With applications to the Korteweg-de Vries Equation," J. Computational Physics, vol. 134, no. 2, pp. 316-331, July 1997.
- W. M. Kahan and R. Li, "Composition constants for raising the orders of unconventional schemes for ordinary differential equations," Mathematics of Computation, vol. 66, no. 219, pp. 1089-1099, July 1997.
- W. M. Kahan, "Analysis and refutation of the LCAS," ACM SIGNUM Newsletter, vol. 26, no. 3, pp. 2-15, July 1991.
- J. Demmel and W. M. Kahan, "Accurate singular values of bidiagonal matrices," SIAM Journal on Scientific and Statistical Computing, vol. 11, no. 5, pp. 873-912, Sep. 1990.
- W. M. Kahan, "Branch cuts for complex elementary functions, or much ado about nothing's sign bit," in The State of the Art in Numerical Analysis: Proc. 3rd Joint IMA/SIAM Conf., A. Iserles and M. J. D. Powell, Eds., Institute of Mathematics and Its Applications Conference Series, Vol. 9, Oxford, England, UK: Oxford University Press, 1987, pp. 165-211.
- W. J. Cody, J. T. Coonen, D. M. Gay, K. Hanson, D. Hough, W. M. Kahan, R. Karpinski, J. Palmer, F. N. Ris, and D. Stevenson, "A proposed radix- and word-length-independent standard for floating-point arithmetic," ACM SIGNUM Newsletter, vol. 20, no. 1, pp. 86-100, Jan. 1985.
- W. M. Kahan, "Mathematics written in sand," in Proc. Joint Statistical Meeting of the American Statistical Association, Alexandria, VA: American Statistical Association, 1983, pp. 12-26.
- W. M. Kahan, B. N. Parlett, and E. Jiang, "Residual bounds on approximate eigensystems of nonnormal matrices," SIAM J. Numerical Analysis, vol. 19, no. 3, pp. 470-484, June 1982.
- C. Davis, W. M. Kahan, and H. F. Weinberger, "Norm-preserving dilations and their applications to optimal error bounds," SIAM J. Numerical Analysis, vol. 19, no. 3, pp. 445-469, June 1982.

## Awards, Memberships and Fellowships

- National Academy of Engineering (NAE) Member, 2005
- American Academy of Arts and Sciences Member, 2003
- IEEE Emanuel R. Piore Award, 2000
- SIAM John von Neumann Lecture Prize, 1997
- Association for Computing Machinery (ACM) Fellow, 1994
- SIAM Activity Group Linear Algebra Best Paper Prize, 1991
- ACM A.M. Turing Award, 1989
- ACM SIGNUM George E. Forsythe Memorial Award, 1972