RE: Another proposal for a "split" function to complement "mid"
If I understand correctly, we want to have approximately sqrt(a,b) when a and b are large, and approximately (a+b)2/ when a and b are small, but in this proposal, if a >> b, then (a+b)/2 >> sqrt(ab), hence we would get asymptotically a/4 instead of sqrt(ab).
I think what Michel meant was geometric mean 2/(1/u + 1/v) = 2uv/(u+v), where u = (a+b)/2 and v =sqrt(ab). This will lead to approximately sqrt(ab) when a >> b and a and b are large and to (a+b)/2 when a >>b and a and b are small -- just as John said we want.
-----Original Message-----
From: stds-1788@xxxxxxxx [mailto:stds-1788@xxxxxxxx] On Behalf Of Michel Hack
Sent: Monday, March 19, 2012 9:52 AM
To: stds-1788
Subject: Another proposal for a "split" function to complement "mid"
How about the following fairly simple idea:
* If interval contains zero, return AM (Arithmetic Mean)
* Otherwise, return AM(AM, GM) where GM is the signed Geometric Mean.
Basically this is 1.5 steps of the AGM.
Michel.
---Sent: 2012-03-19 15:55:30 UTC