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

Professor Emeritus of Mathematics, and of E.E. & Computer Science

863 Evans Hall (Math), and 411 Soda Hall (CS)

Now that I am "retired", I work in my

offices sporadically at least once or

twice a week during each semester.

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.

Better ways to communicate with me are ...

... by paper mail: EECS Dept., MS#1776, Univ. of Calif., Berkeley CA 94720-1776

... by telephone (or leave a message for me to call back), or

... by visiting when I am in my office (telephone me first).

Use e-mail only if you must; but be advised that the University's

e-mail is not so secure that you can trust its confidentiality.

**7094II System Support for Numerical Analysis***IBM SHARE Secretarial Distribution*SSD#159 Item C-4537 (1966), and in*Error in Numerical Computation*, Univ. of Mich. Eng'g Summer Conf'ce #6818*Numerical Analysis*(1968) (A retyped reproduction)(PDF file)**Calculating the Singular Values and Pseudo-Inverse of a Matrix**- (with G.H. Golub), pp. 205-224,
*J. SIAM Numer. Anal.*SER. B. Vol. 2 #2 (1965)(PDF file) **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. **A Family of Anadromic Numerical Methods for Matrix Riccati Differential Equations**- (with Ren-Cang Li),
*Mathematics of Computation,*Vol. 81 #227, Jan. 2012, pp. 233-265.

(PDF file) **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 here:) (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)

- Notes for Math. 110, Linear Algebra, Spring Semester 2002.
- Notes for Math. H 110, Honors Linear Algebra, Fall Semester 2000.
- Notes for Math. 221, Matrix Computations, Fall Semester 1996.
- Notes for Math. H 90, Putnam Problems Practice, Fall Semester 2007.
- Notes for Math. 55, Discrete Math., Spring Semester 1999.
- Supplementary Notes for Math. 128 A/B, Numerical Analysis.
- Supplementary Notes for Math. (H)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 (1985) for binary floating-point arithmetic, including ...
- ... why we needed a floating-point standard (PDF file)
- The Improbability of Probabilistic Error Analyses for Numerical Computations (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)
- MATLAB programs to manipulate the Cyclic Binary Gray Codewords. (Text files)
- SIAM's John von Neumann Lecture for 1997 (PDF file)
- 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)
- LETTER: About Infinity, for Schoolteachers (PDF file)
- LETTER: About Zeno's Dichotomy and Paradox (ASCII file)
- HISTORY: 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)
- AUTOMOTIVE: Simple Transistorized Ignition Retrofits to Old Cars (PDF file)
- AUTOMOTIVE: A Device to Warn When Coolant is Low in a Car's Radiator (PDF file)
- The Numerical Analyst as Computing Curmudgeon (PDF file)
- Questions about Teaching Technical Topics Online (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)
- Poster Presentation to Householder Symposium XVIII (PDF file)
- Three-minute Oration to Householder Symposium XVIII (text 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)
- What I Do (PDF file)
- Back to the Future of Undebuggable Floating-Point Software in Science and Engineering (PDF file)
- Presented to "Matrix Computations and Scientific Computing" Seminar 9 Sept. 2009 (PDF file)
- Needed Remedies for the Undebuggability of ... Floating-Point Computations ... (PDF file)
- Desperately Needed Remedies for the Undebuggability of ... Floating-Point Computations ... (PDF file)
- Desperately Needed Remedies for the Undebuggability of ... Floating-Point Computations ... as presented at Heidelberg Laureates Forum #2 (PDF file)
- on Pete's Unsung Contribution to IEEE Standard 754 for Binary Floating-Point
(PDF file)

for a Panel on the Future of Numerical Linear Algebra: Undebuggable (PDF file) - Deflations Preserving Relative Accuracy, for IWASEP IX in Napa 4 June 2012 (PDF file)
- For the ACM's Turing Centenary Celebration 15-16 June 2012 in San Francisco (PDF file)
- A Numerical Analyst thinks about Artificial Intelligence & Deep Learning (PDF file)
- For ARITH 23: Critiques of John L. Gustafson's Unum Computation and SORN arithmetic (PDF file)
- ... the Critiques' gory details: (Unums' pdf) & (SORN's pdf)

Old postings above get updated and new ones get added from time to time.

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