[scilab-Users] intg: results differ substantially from those from Wolfram Alpha, which are correct?

[Ginters Bušs]

> >
> > Thanks. I like your insistance in that discussion, Sam.
> >
> > Although a "known-limitation-of-current-algorithm" might be a correct
> > description of the current algorithm, it nevertheless does not help
> > much when one wants the algorithm to give the correct solution and
> > observes that a guy like Wolfram has apparently has done something
> > about this issue: for y given function, Scilab's intg/integrate gives
> > ok value for bounds (-50,50), but screws up for (-100,100) and larger
> > bounds, which I consider still pretty narrow. On the contrary, Wolfram
> > Alpha
> >
> >
> http://www.wolframalpha.com/input/?i=integration&a=*C.integration-_*Calculator.dflt-&f2=%281%2Fsqrt%282*pi%29%29*log%28abs%281%2B.1*x%29%29*exp%28-%28x
> ^2%29%2F2%29&x=0&y=0&f=Integral.integrand_%281%2Fsqrt%282*pi%29%29*log%28abs%281%2B.1*x%29%29*exp%28-%28x^2%29%2F2%29&f3=-infinity&f=Integral.rangestart_-infinity&f4=%2Binfinity&f=Integral.rangeend_%2Binfinity&a=*FVarOpt.1-_**-.***Integral.variable---.**Integral.rangestart-.*Integral.rangeend---
> >
> > gives ok values for bounds (-50,50), (-100,100), (-1000,1000) and it
> > allows to directly use infinite bounds and get ok result (interim
> > bounds like (-1e9,1e9) are not ok). I consider this a superior
> > solution. If Wolfram can, why shouldn't Scilab try? The status quo
> > might hurt Scilab's reputation in the domain in long run.
> >
> > Gin.
>
> On Tue, May 24, 2011 at 12:07 PM, Calixte Denizet <
> calixte at contrib.scilab.org> wrote:
> Hi Ginters,
>
> You could use something like:
> subintlen=1;
> xmin=-1e2;
> xmax=1e2;
> out=0;
> l=list(f,1,.1);// to avoid to create again the list
> for i=xmin:subintlen:(xmax-subintlen);out=out+intg(i,i+subintlen,l);end;
>
>> out
>>
>> Calixte
>
>
>
> This is a natural, direct treatment of the problem and seems absolutely
sufficient for my current applications.
Thanks to all.

Gin.
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