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From: dpb on 6 Aug 2010 10:00
David Romero-Antequera wrote:
....

> For the exponential series, the error goes as (dt^(m+1))/factorial(m+1).
> Here I used m as the accuracy goal (in this case, 1e-9), and computed
> the number of terms needed to achieve AT LEAST this accuracy using
> n=fix(L10/ldt). This is by no means a good approximation of the real
> formula, but it is, however, always higher than the real one, which is
> good. On the other hand, I needed an upper number of Taylor terms, and I
> just decided to use m as well.
>
> The real intention here was to optimize time, and then I will improve
> accuracy from there. However, it seems that this is not a good option,
> because Taylor series converge really slow, and I will need a lot of
> terms to achieve a good accuracy, which means an slower algorithm.
>
> I'm trying some other things, but if anyone else have a better idea, I
> surely would like to try it. :)

I've not followed this thread at all, but if it's approximations you're
looking for, I'd suggest Abramowitz and Stegun as the font of knowledge
to investigate...

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