RE: [boost] Re: Numerical Integration - continued

From: Matt Sutton (matt.sutton_at_[hidden])
Date: 2002-10-25 10:11:19

> -----Original Message-----
> From: Martin Weiser [mailto:weiser_at_[hidden]]
> Sent: Friday, October 25, 2002 1:05 AM
> 
> On Freitag, 25. Oktober 2002 08:04, Daryle Walker wrote:
> 
> > There are at least four ways to address the domain values:
> >
> > 1.	initial x, final x, and the number of intervals between them
> > 2.	initial x, final x, and the interval size
> > 	A.	note that the interval size may not fit evenly
> 
> Probably a common case if evenly spaced data is available. 1 
> seems to be a 
> more or less trivial special case of 2.
> 
> > 3.	initial x, final x, and letting the algorithm decide 
> intermediate
> > x's A.	this is for an adaptive algorithm
> > 	B.	requires the y's to be given by a function/functor
> 
> Probably the most apropriate case if the data is indeed given by a 
> function/functor. Also allows for the most sophisticated, efficient, 
> robust, and accurate algorithms. That's the case I'm most 
> interested in.

[snip]

At a minimum, we would need to supply an error criterion for case 3 as well,
with perhaps a suitable default value.  From what I remember, exactly how
you compute the error within different algorithms can be a small bone of
contention among the purists. I don't know if delagating error computations
to a policy class such that users could supply specialized methods would be
overkill or not.

3.	initial x, final x, error

Matt