Re: [boost] Re: Numerical Integration - continued

From: Martin Weiser (weiser_at_[hidden])
Date: 2002-10-24 07:26:29

On Donnerstag, 24. Oktober 2002 11:37, Matthias Troyer wrote:
> On Thursday, October 24, 2002, at 11:00 AM, Martin Weiser wrote:
> > On Mittwoch, 23. Oktober 2002 21:52, Matthias Troyer wrote:

> >> i) 1D integration of a function with x-points determined by the
> >> algorithm (e.g. Romberg integration)
> >>
> >> ii) Integration of first order ODEs by some algorithm (e.g.
> >> Runge-Kutta)

> > Agreed. Let me add that I think the interface to i) is more or less
> > straightforward, while the interface to ii) is much more complex and
> > less
> > obvious.
>
> I agree fully. One problem for the interface of ii) is that some
> algorithms need more than one starting point. Should this discussion be
> about both topic or should we first focus on the simpler case i)?

Both topics are different enough to justify different interfaces, and 
hence can be handled independently. I'd prefer fixing and implementing i) 
as soon as it's ready, without waiting for ii) to mature. 

Multistepmethods requiring more than one starting point is one of the less 
demanding problems. More difficult should be the linear algebra part: How 
should vectors and (for implicit propagators) matrices be represented? Do 
we rely on uBlas, MTL3, valarray, ....?

Yours,
Martin

-- 
Dr. Martin Weiser            Zuse Institute Berlin
weiser_at_[hidden]                Scientific Computing
http://www.zib.de/weiser     Numerical Analysis and Modelling