• May 06, 2021, 05:53:04 PM

### Author Topic:  How to Get More Than 3 Series Approximation Terms?  (Read 1390 times)

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#### claude

• 3f
• Posts: 1849
##### Re: How to Get More Than 3 Series Approximation Terms?
« Reply #15 on: December 21, 2017, 02:37:04 AM »
The expansion factor of two-real-interval complex intervals is worse than sqrt(2): here's an example from the intpakX Maple package site: http://www2.math.uni-wuppertal.de/~xsc/software/intpakX/example_compl.html

the example is B(1 + 0i, 1) * B(-1+1i, 1), the results are:
B(-2.00 + 2.00 i, 5.66) -- two real intervals
B(-1.00 + 1.00 i, 3.41) -- regular intpakX
B(-1.39 + 1.39 i, 2.97) -- area optimized intpakX

not sure what the license for intpakX is, but copyright applies to creative expression of ideas, not ideas themselves, so reimplementation in a non-Maple language may be fine if it's more than simple copy/paste

#### knighty

• Fractal Feline
• Posts: 198
##### Re: How to Get More Than 3 Series Approximation Terms?
« Reply #16 on: December 21, 2017, 09:09:44 AM »
if using c++, how about the boost interval stuff?

http://www.boost.org/doc/libs/1_66_0/libs/numeric/interval/doc/interval.htm

its a lot of reading about a lot of stuff im not familiar with
though one good thing is being template-based it sounds like you can use your own types with it
As Claude said, that library uses "two points interval arithmetic" which is not well suited for complex numbers. The "midpoint-radius intervals" are much better. Unfortunately I didn't find a publicly available library that uses it... There is the Arb library, but it is not exactly what we need.

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