Re: [Axiom-mail] Exponential Integral (UNCLASSIFIED)

[Tim Daly-3]

Steven,

I found your paper when I was looking for good fit values for E1(x).
I'd be happy to get your newer fit numbers.
I'll rewrite the Axiom code to use them.

Tim Daly
Axiom Lead Developer

Segletes, Steven (Civ,ARL/WMRD) wrote:

>
> Classification: _* UNCLASSIFIED*_
> Caveats: NONE
>  
> I was tickled to find mention of my exponential integral (E1(x))
> fitting algorithm at
> _http://www.axiom-developer.org/axiom-website/patches/20080119.01.tpd.patch_
> .  As noted there, the accuracy of my published fit is only 4 decimal
> places.  Years ago, I  extended that original fit to greater precision
> (with more parameters of course), if it is of use to anyone, though I
> have not published the extensions.  I do not subscribe to your
> maillist, but am happy to provide the fits, should you provide your
> request to me at steven@....
>
> Regards,
> Steven Segletes
> U.S. Army Research Laboratory
> Aberdeen Proving Ground, MD 21005-5066
>
>
>
>  
> Classification: _* UNCLASSIFIED*_
> Caveats: NONE
>
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[Tim Daly-3]

If you know of any other fits to interesting functions I'd appreciate a
pointer to the work.
Finding high quality, numerically stable, smooth piecewise fits is a
challenge.

Tim Daly
Axiom Lead Developer

Segletes, Steven (Civ,ARL/WMRD) wrote:

>
> Classification: _* UNCLASSIFIED*_
> Caveats: NONE
>  
> I was tickled to find mention of my exponential integral (E1(x))
> fitting algorithm at
> _http://www.axiom-developer.org/axiom-website/patches/20080119.01.tpd.patch_
> .  As noted there, the accuracy of my published fit is only 4 decimal
> places.  Years ago, I  extended that original fit to greater precision
> (with more parameters of course), if it is of use to anyone, though I
> have not published the extensions.  I do not subscribe to your
> maillist, but am happy to provide the fits, should you provide your
> request to me at steven@....
>
> Regards,
> Steven Segletes
> U.S. Army Research Laboratory
> Aberdeen Proving Ground, MD 21005-5066
>
>
>
>  
> Classification: _* UNCLASSIFIED*_
> Caveats: NONE
>
> ------------------------------------------------------------------------
>
> _______________________________________________
> Axiom-mail mailing list
> Axiom-mail@...
> http://lists.nongnu.org/mailman/listinfo/axiom-mail
>  

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[Segletes, Steven (Civ,ARL/WMRD)]

Classification:  UNCLASSIFIED
Caveats: NONE

Tim,

I have attached a PDF writeup detailing the more accurate fits to E1(x),
relative to those presented in ARL-TR-1758.  My actual fits are to F1 =
[x exp(x) E1(x)] which spans a functional range from 0 to 1.  The best
accuracy I have been yet able to achieve, defined by limiting the value
of [(F1)_fit - F1]/F1 over the domain, is approximately 3.1E-07 with a
12-parameter fit, which unfortunately isn't quite to 32-bit
floating-point accuracy.  Nonetheless, the fit is not a piecewise fit,
but rather a single continuous function over the domain of nonnegative
x, which avoids some of the problems associated with piecewise domain
splicing.

Also, I have not, as yet, had the need to look at other functions that
could stand improved fitting, but you could always suggest a function to
get me thinking about it.

Kindest regards,
Steven Segletes
US Army Research Laboratory
Aberdeen Proving Ground, MD 21005-5066


  Classification:  UNCLASSIFIED
Caveats: NONE



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