[std-interval] Re: ESA Study on Interval Methods for Inegration

[Markus Neher]

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>
> Content-Type: text/plain; charset=ISO-8859-1; format=flowed
> 
> 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