[VA] SRC#001 - Spiky Integral

[Valentin Albillo]

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Hi, Albert:

Albert Chan Wrote:Hi Valentin, Thanks for the check.

You're welcome.

Quote:The fact that two integral only match 42 digits does not mean anything. The spike formula asked for full spike area. [...]You might like to try the spike formula again, for N = 1000. For I(1000), you have a correct value to match against ...

I'll do it soon, when I get home in a few hours.

Quote:Rounded to 45 digits, it match Valentin value exactly

Of course. That's why I stated "(all 48 decimal digits shown are correct)" ... :-) ... (the 48 decimal digits mentioned include the three initial zeros as well).

Quote:Is it possible to explain how the integration code work ? How does it handle so many spikes ?

I developed the code myself as a program for the HP-71B, good for 12 digits and easily surpassing the speed of the assembly-language Math ROM's INTEGRAL keyword, then ported it nearly verbatim to a multiprecision environment, which is the version I've used to produce the results I've posted in this thread.

The code was intended to be included in one of my PDF Datafile articles some 10 years ago, as explaining it and providing relevant examples would take at least some 10-12 pages. Alas, for reasons which I won't repeat here the article was never submitted for publication and remains unpublished to this day.

If (and when) I can find some adequate place where to publish it, I'll post an announcement here for interested people (like yourself) to download it for free.

Thanks for your interest and regards.
V.
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