Dublin Area Mathematics Colloquium

Slides (1up PDF 1.1 MB)

Printable Slides (4up PDF 0.74 MB)

NOTES

Here are some notes and papers that show that writing accurate, efficient, and robust numerical software is a task best left to experts.

Two Simple Statistical Calculations & Climategate

These notes discuss the difficulties that can arise in calculating the mean and standard deviation of a set of floating point numbers. A section has been added that analyzes the errors in one of the programs written by a member of the Climate Research Unit at the University of East Anglia. Statistical-Calculations-and-ClimateGate

The original paper and data for the Sea Surface Heights problem, discussed in these notes and the slides above, are here He & Ding -- OceanHeights.pdf, etaana.dat

Argument Reduction.

This 1992 paper by K.C. Ng shows how difficult it is to compute sin(x) for large arguments Ng--ArgReduction.pdf (78KB) . Here is a LaTeXed version of this paper that is a little easier to read Ng--ArgReduction.pdf .

Class Notes

Notes on my Numerical Algorithms webpage may be of interest:

Master of Computational Science : Numerical Algorithms

Books and Papers (Incomplete) : References

Software : The software mentioned in the talk is on this page. This is a page of mostly free software I have found useful over the years.

Seventh Conference on Real Numbers and Computers, July 2006. http://rnc7.loria.fr/ This and previous conferences have many papers on the latest ideas in floating point arithmetic.

Dublin Area Mathematics Colloquium

Floating Point Arithmetic

or

You Can't Always Count on Your Computer