HP49-50G Lambert function
10-21-2020, 12:13 PM (This post was last modified: 06-23-2021 01:00 PM by Albert Chan.)
Post: #13
 Albert Chan Senior Member Posts: 2,142 Joined: Jul 2018
RE: HP49-50G Lambert function
(10-21-2020 02:54 AM)Albert Chan Wrote:  >>> a = -log(2)/2
>>> 1/eW(a, y=0.2)
0 0.2
1 (0.240506189867-0j)
2 (0.24956480343-0j)
3 (0.24999902269-0j)
4 (0.249999999995-0j)
(4.0000000000000018+0j)

There is a reason I picked guess for y below -a (≈ 0.346574)
If guess is above -a, Newton's formula, y ← (y+a)/(log(y)+1), might converge to e^W0 (*)
If guess is below -a (but still positive), it always converge to e^W-1

see plot {(y + -ln(2)/2)/(ln(y)+1), y}, y = 0 .. 1/e

(*) it might still converge to e^W-1, with iterations involving complex numbers.
First iteration overshooted to y<0, then all iterations turned complex.
I tried it, the cut-off is guess ≈ 0.365414
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 Messages In This Thread HP49-50G Lambert function - Gil - 10-17-2020, 08:42 PM RE: HP49-50G Lambert function - Gil - 10-18-2020, 10:22 AM RE: HP49-50G Lambert function W(z) - Gil - 10-19-2020, 09:06 AM RE: HP49-50G Lambert function - Gil - 10-19-2020, 09:13 AM RE: HP49-50G Lambert function - Albert Chan - 10-20-2020, 01:48 AM RE: HP49-50G Lambert function - Gil - 10-19-2020, 09:40 AM RE: HP49-50G Lambert function - Gil - 10-20-2020, 08:28 AM RE: HP49-50G Lambert function - Gil - 10-20-2020, 08:42 AM RE: HP49-50G Lambert function - Albert Chan - 10-20-2020, 04:40 PM RE: HP49-50G Lambert function - Gil - 10-20-2020, 10:44 PM RE: HP49-50G Lambert function - Albert Chan - 10-21-2020, 02:54 AM RE: HP49-50G Lambert function - Albert Chan - 10-21-2020 12:13 PM RE: HP49-50G Lambert function - Gil - 10-21-2020, 11:44 AM

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