ESSAY: Ten digit algorithms

[AM] (8 august 2005) This message appeared in the "NA Digest newsletter":

 "I have written an essay, presented as the Mitchell Lecture at the
 recent Dundee meeting, that advocates the production of Ten Digit
 Algorithms, defined by the conditions "Ten digits, five seconds,
 and just one page".  The essay comes with 32 Matlab examples.
 I imagine these views may provoke some strong reactions among NA
 Digest readers.  Would interested parties like to take a look at
 http://web.comlab.ox.ac.uk/oucl/work/nick.trefethen/tda.html and
 send me any comments?  If the responses are interesting I may post
 a follow-up note later on.

              Nick Trefethen, Oxford University"

Both the essay and the associated examples present a nice challenge IMHO for anyone interested in numerical analysis and Tcl.

[RS] isn't quite sure - can the following script be considered the minimal compliant "algorithm"? :^)
 set tcl_precision 10
 after 5000

[Lars H]: No, because it will take slightly longer than five seconds to run. :-) Like the "one page", "five seconds" is an upper bound (whereas the "ten digits" is a lower bound). Also, and more importantly, the algorithms still have to be algorithms: ''they must actually compute something''. Hence your program is perhaps rather the minimal ''noncompliant'' program for computing the empty string.

[KBK] We have a few of the classic ten-digit algorithms in Tcllib.
::[math::calculus]::Romberg fits on a page if the parameter checking
is stripped (and the default precision to request, coincidentally, 
is ten digits).  I suspect that Richard could reduce
the code in [Constrained minimisation in one dimension] to a page, and that's another
classic.

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