Re: [boost] Re: Numerical Integration - continued

From: Martin Weiser (weiser_at_[hidden])
Date: 2002-10-24 12:14:33

On Donnerstag, 24. Oktober 2002 18:13, Neal D. Becker wrote:
> >>>>> "Dan" == Dan Mcleran <dan.mcleran_at_[hidden]> writes:
>
>     Dan> 1D Numerical Integration

>     Dan> Here are what I would suggest to be the high-level
> requirements for Dan> whichever direction we go for 1D numerical
> integration:
>
>     Dan> 1. They must be able to integrate a user-defined function from
> point a to Dan> point b in increments of deltax.
>
> I think it should be more general.  deltax does not need to be fixed.
> The romberg integration routine I am using chooses the points
> adaptively.

I'd like to support this opinion. As elaborated by Matt in a different 
posting, adaptive methods choosing the integration nodes on their own may 
be far more efficient, accurate, and robust than straightforward uniform 
ones.

If the interface requires the user to supply integration nodes, the 
library asks too much of him. Many users will supply simple integration 
nodes (e.g. equidistant) in favor of suitable ones, and obtain suboptimal 
results.

Even worse would be to enforce uniform integration by providing just a dx 
to adjust.

Yours
Martin

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