Em domingo, 6 de março de 2011 às 06:18:29 UTC-3, glen herrmannsfeldt escreveu:
> nm...@cam.ac.uk wrote:
> (snip on integration algorithms)
> > Rather longer ago that that, I was working on multi-dimensional
> > scaling, which has the property that it has a set of fairly
> > well-defined local minima, but where discontinuities are dense
> > (but in the same direction as the slope). Steepest descents
> > worked; little else did.
> > There is a fairly general rule that the less well-behaved the
> > problem you have, the cruder a method you must use, because all
> > fancy methods need to make more assumptions. Runge-Kutta is a
> > bit odd, but also blows up quite spectacularly given a hostile
> > enough function. For some, there is little option but simple
> > step-by-step approximation.
> I always liked Gaussian quadrature, though its assumptions
> likely cause problems with some functions. With no prediction,
> it shouldn't get too confused. The old trick of running with
> different order and checking that the result isn't too different
> should still work.
> > As a side-note, IBM SSP contained the only matrix inversion code
> > that I have ever seen that succeeded in inverting a singular 3x3
> > matrix - AND returning elements of the same order as the input!
> > Impressive.
> The code is still around, if anyone wants to try it.
> > Harwell and NAG didn't like the matrix at all :-)
> -- glen

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