[std-interval] Re: Std-interval Digest, Vol 7, Issue 5

[Ray Moore]

Markus and All:

Indeed, among the conclusions of the ESA study, we find:
"All interval integrators which have been tested in this work try to avoid 
the wrapping effect using a linear expansion of the solution of the ODE with 
respect to the initial conditions. However, the works of Berz and Makino 
showed that important improvements on the control of this effect cam be 
achieved when higher order methods on initial conditions are applied. As a 
consequence, further intensive investigations should be accomplished, aimed 
at estimating the performances of such promising methods on the integration 
of typical space-related problems."

Ray Moore


----- Original Message ----- 
From: <std-interval-request at compgeom.poly.edu>
To: <std-interval at compgeom.poly.edu>
Sent: Friday, August 18, 2006 3:00 PM
Subject: Std-interval Digest, Vol 7, Issue 5


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>   1. Re: ESA Study on Interval Methods for Inegration (Markus Neher)
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>
> ----------------------------------------------------------------------
>
> Message: 1
> Date: Fri, 18 Aug 2006 10:04:43 +0200
> From: Markus Neher <markus.neher at math.uni-karlsruhe.de>
> Subject: [std-interval] Re: ESA Study on Interval Methods for
> Inegration
> To: std-interval at compgeom.poly.edu
> Message-ID: <44E5749B.6050008 at math.uni-karlsruhe.de>
> Content-Type: text/plain; charset=us-ascii
>
> 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
>
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> End of Std-interval Digest, Vol 7, Issue 5
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