[std-interval] Re: ESA Study on Interval Methods for Inegration
Markus Neher
markus.neher at math.uni-karlsruhe.de
Fri Aug 18 11:04:43 PDT 2006
Dear colleagues,
> Message: 1
> Date: Wed, 16 Aug 2006 15:24:41 -0700
> From: "Lawrence Crowl" <lawrence.crowl at gmail.com>
> Subject: Re: [std-interval] FW: applications
> To: "For discussions concerning the C++ standardization of intervals"
> <std-interval at compgeom.poly.edu>
> Message-ID:
> <90228e530608161524v5f4b390dk2998b0afe741aad4 at mail.gmail.com>
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>
> I'm not an expert in the domain, but my read of the conclusions
> is that the interval approach wasn't helpful. Apparently, the
> integration process failed far earlier than non-interval integration.
> How are we interpreting the conclusions differently?
In my opinion, the ESA study only shows that two existing interval
solvers for ODEs failed earlier than non-interval integration.
It is well known that validated integration with Taylor model methods
performes much better for these IVPs than the tested interval solvers,
see for example
@article{HoBeMa03a,
author = "J. Hoefkens and M. Berz and K. Makino",
title = "Controlling the Wrapping Effect in the Solution of
{ODEs} for Asteroids",
journal = "Reliable Computing",
volume = "9",
pages = "21-41",
year = "2003",
}
Regards,
Markus
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