William Kahan

Ph.D. (Math., University of Toronto, 1958)

Professor of Mathematics, and of E.E. & Computer Science
863 Evans Hall (Math), and 733 Soda Hall (CS)
Phone: (510) 642-5638 (rings in both offices)
E-mail to me at this address obfuscated to diminish spam:
wkahan at (omit underscores) E_E_C_S_D0T_B_E_R_K_E_L_E_Y_D0T_E_D_U

My e-mail is read at most once every week or two. There is much too much of it.

Students who wish to communicate with me in my capacity as Computer Science Ombudsman
may do so by paper mail, by telephone (or leave a message for me to call back), or by
visiting when I am in my office, or by e-mail; but be advised that the University's
e-mail is not so secure that you can trust its confidentiality.

Classes for Fall Semester 2007:
Math. H90: Putnam Problems Practice Seminar, Mon. 4 - 6 pm. 71 Evans Hall
Math. H90 Discussions: Fri. 8 - 10 am. 75 Evans Hall
Conducted jointly with Prof. Vera Serganova.
See the class web page.

Tentative Office Hours: 1:15 - 2 pm. Mon. in 733 Soda, 10:10 - 11 am. Wed. & Fri. in 863 Evans

Awards etc.

Keynote Speaker at IEEE Sponsored ARITH 17 Symposium on Computer Arithmetic dedicated to W. Kahan, 2005
Foreign (Canadian) Associate, National Academy of Engineering, U.S.A., 2005
Distinguished Mentor of Undergraduate Research in the College of Letters & Science, 2004
American Academy of Arts & Sciences, 2003
IEEE Emanuel R. Piore Award, 2000
Honorary Doctor of Mathematics, University of Waterloo, Canada, 1998 (PDF file)
Soc. Indust. & Appl. Math., 1997 John von Neumann Memorial Lecture
ACM Fellow, 1994
Honorary Doctor of Mathematics, Chalmers Inst., Goteborg, Sweden, 1993
SIAM Activity Group on Linear Algebra, Prize for 1988-90's Outstanding Paper (with J. Demmel), 1991
ACM Turing Award, 1989
ACM 1st G. E. Forsythe Memorial Award, 1972

Selected Publications

Analysis and Refutation of the LCAS

ACM SIGNUM Newsletter, Vol. 26, No. 3, July 1991, pp. 2-15.
Also, ACM SIGPLAN Notices, Vol. 27, No. 1, January 1992, pp.61-74.

Accurate Singular Values of Bidiagonal Matrices

(with J. Demmel), SIAM J. Scientific Statistical Computation, Vol. 11, No. 5, 1990, pp. 873-912.

Branch Cuts for Complex Elementary Functions, or Much Ado About Nothing's Sign Bit

in The State of the Art in Numerical Analysis, (eds. Iserles and Powell), Clarendon Press, Oxford, 1987.

A Wordsize- and Radix-Independent Standard for Floating-Point Arithmetic

(with W. J. Cody et al.), IEEE Micro, August 1984, pp. 86-100.

Mathematics Written in Sand

Proc. Joint Statistical Mtg. of the American Statistical Association, 1983, pp. 12-26.
(A legible reproduction is available below)(PDF file)

Norm-Preserving Dilations and Their Applications to Optimal Error Bounds

(with C. Davis and H. F. Weinberger), SIAM J. Numerical Analysis, Vol. 19, 1982, pp. 445-469.

Residual Bounds on Approximate Eigensystems of Nonnormal Matrices

(with B. N. Parlett and E. Liang), SIAM J. Numerical Analysis, Vol. 19, 1982, pp. 470-484.

Unconventional Schemes for a Class of Ordinary Differential Equations -- With Applications to the Korteweg-deVries Equation

(with Ren-Cang Li), J. Computational Physics, Vol. 134, 1997, pp. 316-331.

Composition Constants for Raising the Orders of Unconventional Schemes for Ordinary Differential Equations

(with Ren-Cang Li), Math. of Computation, Vol. 66, 1997, pp. 1089-1099.

Pinchings and Norms of Scaled Triangular Matrices

(with Ren-Cang Li & Rajendra Bhatia), Linear & Multilinear Algebra, Vol. 50, 2002, pp. 15-21.

Is there a small skew Cayley transform with zero diagonal ?

Linear Algebra and its Applications 417 (2006) pp. 335-341.
(A version with fewer misprints is available below)(PDF file)

Error bounds from extra-precise iterative refinement (with J.W. Demmel et al.)

ACM Transactions on Mathematical Software (TOMS) archive 32, Issue 2 (June 2006) pp. 325 - 351
(PDF file)

Files available from this homepage, last updated 27 Aug. 2007

Notes for Math. 110, Linear Algebra, Spring Semester 2002.
Notes for Math. 221, Matrix Computations, Fall Semester 1996.
Notes for Math. H 90, Putnam Problems Practice, Fall Semester 2007.
Notes for Math. H 110, Honors Linear Algebra, Fall Semester 2000.
Notes for Math. 55, Discrete Math., Spring Semester 1999.
Supplementary Notes for Math. 128, Numerical Analysis.
Supplementary Notes for Math. 185, Analytic Functions of Complex Variables.
Abstracts of the following papers, updated 11 Sept. 2005.(IBM PC Extended ASCII text)
Documents relating to IEEE standard 754 for binary floating-point arithmetic, including ...
... why we needed a floating-point standard (PDF file)
The Improbability of Probabilistic Error Analyses for Numerical Computations (PostScript) (PDF file)
SRTEST is a Fortran/DOS program for testing accuracy of floating-point division
Pi-related programs (C and lisp)
How to Test Whether SQRT is Rounded Correctly (PostScript)
Test programs for the ix87's FIST (Float-to-Integer STore) instruction
Beastly Numbers, a paper about two different computers upset in the same way by the same two floating-point numbers
On the Monotonicity of some Computed Functions (PDF file)
Approximate Trisection of an Angle (PDF file)
Miscalculating Area and Angles of a Needle-like Triangle (PDF file)
Roundoff Degrades an Idealized Cantilever (PostScript)
Roundoff Degrades an Idealized Cantilever (PDF file) See Abstracts above for programs.
Gregorian calendar and MATLAB programs for it. (Text files)
SIAM's John von Neumann Lecture for 1997 (PostScript)
How JAVA's Floating-Point Hurts Everyone Everywhere (PDF file)
Matlab's Loss is Nobody's Gain (PDF file)
Is there a Small Skew Cayley Transform with Zero Diagonal? (PDF file) Presentation version:(PDF file)
Marketing vs. Mathematics (PDF file) (PostScript)
Mathematics Written in Sand (reproduced legibly)(PDF file)
About Infinity, for Schoolteachers(PDF file)
How Blabber-Mouth U-boats Got Sunk in World War II(PDF file)
What has the Volume of a Tetrahedron to do with Computer Programming Languages?(PDF file)
Simple Transistorized Ignition Retrofits to Old Cars(PDF file)
The Numerical Analyst as Computing Curmudgeon (PDF file)
A Logarithm Too Clever By Half. (Text file)
Why is Floating-Point Computation so Hard to Debug when it Goes Wrong? (PDF file)
How Futile are Mindless Assessments of Roundoff in Floating-Point Computation?(PDF file)
How Futile ... Floating-Point Computation? (Extract presented to Householder Symposium XVI)(PDF file)
On the Cost of Floating-Point Computation Without Extra-Precise Arithmetic(PDF file)
The Baleful Influence of SPEC Benchmarks upon Floating-Point Arithmetic (Presented to SPEC)(PDF file)
A Demonstration of Presubstitution for Infinity/Infinity (PDF file)
Floating-Point Arithmetic Besieged by "Business Decisions" (Presented to ARITH 17) (PDF file)
A Brief Tutorial on Gradual Underflow (Presented to ARITH 17, subsequently augmented) (PDF file)
Circumscribing the Intersection of Two Ellipsoids by an Ellipsoid as Tightly as Possible (PDF file)
Why I can Debug some Numerical Programs You Can't (PDF file)
Old postings above get updated and new ones get added from time to time.

W. Kahan's self-portrait.