Dublin Area Mathematics Colloquium

Slides (1up PDF 1.1 MB)

Printable Slides (4up PDF 0.74 MB)

Notes : Here are notes on a few important topics not covered in the talk, along with some answers to questions raised at the end of the talk. (Nothing here yet, but in the meantime the notes on my Numerical Algorithms webpage may be of interest : Master of Computational Science : Numerical Algorithms)

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 .

References : Books and Papers (Incomplete)

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.

The original paper and data for the Sea Surface Heights problem are here He & Ding -- OceanHeights.pdf, etaana.dat

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