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

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
- NEW! 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
- 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

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:

--Equation-solving, linear and nonlinear

--Eigenvalues/vectors of matrices

--Failure modes of MATLAB's functions for the above

--Palliatives for failure modes; Iterative Refinement

--Other iterative methods

--Integration - Quadrature and ODEs; impediments to error-control

--Simple Elliptic and Parabolic PDEs

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.

Plans: What do you intend to do after you graduate?

Topic choices: List some you think you will need or are curious to learn.

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?

course. A suitable project consists of a scientific paper written well enough

to be publishable in principle. It may explore in greater depth a topic

covered in class, or cover a topic that could have been covered in class

but wasn't. The project can report on an application of numerical methods to

an interesting problem relevant to your intended career. Credit will be

earned not so much for a program as for the mathematical analysis that

justifies it. Why did you choose your program's method(s) instead of others?

How do its results compare with what you intended? If discrepancies occurred,

what have you done about them? When and why should your program's results be

trusted? How do you know?

client or employer explaining how and why your work has been worthwhile.