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Accuarcy-Complex V11.3

GROUPS:

Hey guys,

I just installed V11.3. However, when I am doing numerical calculations, which is a summation. V11.3 would give answers in complex number while I only get answers in real field in any earlier versions, e.g., V11.1 and V11.2. Of course, my input is a real number. Although the imaginary part is extremely small, I am curious how the machine could get a complex number now. Is there any changes in the algorithm for summations in V11.3?

Please see my attachment.

Thanks in advance.

Attachments:
POSTED BY: Zhehao Zhang
Answer
2 months ago

It's from terms like Gamma[100 - 5/0.015`200].

POSTED BY: Michael Rogers
Answer
2 months ago

Yes, I found that too. Thank you.

However, I am wondering what leads to this change?

POSTED BY: Zhehao Zhang
Answer
2 months ago

I don't know for sure. I can see that the result is the same as Exp@LogGamma[100 - 5/0.015`200]. Gamma[] is negative, so LogGamma[] is complex. Gamma[100 - 5/0.015`] (machine precision) now underflows to 0., with an error message, in V11.3. In V11.2, it automatically is promoted to an arbitrary-precision number that can handle such small numbers. This change in handling underflows is a big change in V11.3. It suggests to me that it might be the reason for the difference in your computation, that they changed how Gamma[] is computed in general to handle the change in machine precision computation.

POSTED BY: Michael Rogers
Answer
2 months ago

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