Prof. W. Kahan's Supplementary Notes for Math. 128 A and B, etc.

As of 7 July 2016, these files are available from this web page.
Some date from 2002 or earlier. They are all time-stamped.
Please be sure to get the latest versions.

• Iterative Refinement of the General Symmetric Definite Eigenproblem. PDF file
• The Nearest Orthogonal or Unitary Matrix. PDF file
• Euclid's GCD Algorithm vs. Programs. PDF file
• A Floating-Point Trick to Solve Boundary-Value Problems Faster. PDF file
• Some applications of cross-products. PDF file
• Root-finding ASSIGNMENT: Results were to be handed in by Mon. 5 Feb. 2007. PDF file
• Newton's iteration to a non-simple root of a vector equation. PDF file
• Solutions for Math. 128B's Assignment due Thurs. 6 Apr. 2006. PDF file
• Reflections and Rotations for QR Factorization. PDF file
• Error-Bounds and Stopping Criteria for Real Roots. PDF file
• Error Bounds Associated with Newton's Iteration. PDF file
• Roundoff in Polynomial Evaluation. PDF file
• Four Running Error-Bounds. PDF file
• OLD Notes on Errors and Equation-Solving; 3.5 MB PDF file
• Prof. Ming Gu's Transparencies. PDF files
• Short note on Conjugate Gradients and Successive Overrelaxation. PDF file
• Assignment issued 19 April 2004. Text file
• Take-Home Test, Solutions due Mon. 8 Mar. 2004. PDF file
• Do MATLAB's inv(...), lu(...) etc. have a Failure Mode?. PDF file
• Model Solutions to Three Problems for Math. 128B due Mon. 9 Feb. 2004. PDF file
• 128 Squares of 128 Sqrts. PDF file
• Separating Clouds by a Plane. PDF file
• Prof. Parlett's Note on the QR Iteration. PDF file
• Justification for Matlab's ODE suite. PDF file
• Quick Solution of Two-body Kepler Orbits. PDF file
• Why naive Interval Arithmetic malfunctions on ODEs. PDF file
• Ellipsoidal Error Bounds for Trajectory Calculations. PDF file
• Taylor Series for ODE-solvers' Truncation Error. PDF file
• The SOLVE key on the HP-34C. PDF file
• Plausible but spurious solutions due to roundoff. PDF file
• Plausible but spurious solutions due to roundoff. PostScript file
• The INTEGRATE key on the HP-34C. PDF file
• Supplementary lecture notes on Real Root-finding. PDF file
• Condensed lecture notes on Better Real Root-finding. PDF file
• Numerically stable formulas for the Angle subtended at the eye by neighboring stars. PDF file
• A matrix equation with infinitely many solutions. PDF file
• REFINEIG: a Program to Refine Eigensystems. PDF file
• Abstract for REFINEIG paper. ASCII file
• Notes on Thiele's Reciprocal Differences. IBM PC ASCII file
• Matlab programs for Interpolation and Extrapolation. IBM PC ASCII file
• Idempotent Binary to-and-from Decimal Conversion. PDF file
• An ODE with a terminal condition at infinity. PDF file
• When to Stop Slowly Convergent Iteration? PDF file
• Summing a Slowly Convergent Series (.txt)
• Variance computed in One Pass, PDF file
• To Solve a Real Cubic Equation, PDF file
• How (Not) to Solve a Real Quartic Equation, PDF file
• Accuracy Tests for Polynomials' Zero-Finders, PDF file
• Two Error-Bounds for a Polynomial's Zero, PDF file
• Experimental Quadrature of Improper Integrals, PDF file

Programming: Students are expected to have access to and acquaintance with
MATLAB version 4.2 or later. Student versions are adequate.

Text: Any old Numerical Analysis text that includes the topics to be covered in
this course will serve well enough at least for a start. A text tuned to MATLAB
is "Numerical Computing with MATLAB" by Dr. Cleve Moler. It is available
printed from S.I.A.M, Philadelphia; or the book's 12 chapters and MATLAB
.m files may be downloaded from The Mathworks : click on
"Textbook by Cleve Moler".
~~~~~~~~~~~~~~~~~~~~~~~~~~

Among the topics to be covered in class are these:

These topics have been determined partly by the instructor's inclinations and
partly by the needs expressed by students taking the course. To this end, each
student has submitted an account of his/her background, plans and topic choices.

The instructor's inclinations are revealed by the postings on his web pages.

As an error-analyst, the instructor tends to question computed results:
-- What evidence corroborates a result's claimed or presumed accuracy?
-- If inadequately accurate, how can a result be recomputed more accurately?

A Final Exam was scheduled, but the class has chosen credit by project instead.
Each student should choose a project as soon as possible. If you cannot think
of a suitable project after six weeks, come to the instructor for suggestions.

What kinds of projects can earn credit instead of a final exam?

In effect, a project is practice for a thesis or for a report to your
client or employer explaining how and why your work has been worthwhile.