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Lambert W Function (hp-42s)
05-20-2020, 03:25 PM (This post was last modified: 05-20-2020 05:37 PM by Albert Chan.)
Post: #11
RE: Lambert W Function (hp-42s)
(05-19-2020 12:29 AM)Albert Chan Wrote:  g = lambda y,a: (y+a)/(log(y)+1)
w = lambda x,a: x+(a/exp(x)-x)/(x+1)

Both Newton's iteration formula are equivalent, but going for y converge faster.
(try plotting x*exp(x) vs x*ln(x), 2nd curve slope = 1+ln(x), does not vary as much)

W(a) = x
x * exp(x) = a

Let y = exp(x), we have y * ln(y) = a

Newton's iteration: y ← y - (y*ln(y)-a) / (ln(y)+1) = (y+a) / (ln(y)+1)

When y converged, y = exp(x) = a/x, we have W(a) = ln(y) = a/y
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Messages In This Thread
Lambert W Function (hp-42s) - Juan14 - 05-16-2020, 04:07 PM
RE: Lambert W Function (hp-42s) - Werner - 05-17-2020, 07:56 AM
RE: Lambert W Function (hp-42s) - Werner - 05-17-2020, 08:15 AM
RE: Lambert W Function (hp-42s) - Gerald H - 05-17-2020, 09:29 AM
RE: Lambert W Function (hp-42s) - Werner - 05-18-2020, 08:04 AM
RE: Lambert W Function (hp-42s) - Juan14 - 05-17-2020, 12:12 PM
RE: Lambert W Function (hp-42s) - Juan14 - 05-18-2020, 10:51 PM
RE: Lambert W Function (hp-42s) - Albert Chan - 05-20-2020 03:25 PM
RE: Lambert W Function (hp-42s) - Juan14 - 05-21-2020, 12:09 AM
RE: Lambert W Function (hp-42s) - Werner - 05-22-2020, 11:39 AM
RE: Lambert W Function (hp-42s) - Werner - 05-23-2020, 04:20 AM
RE: Lambert W Function (hp-42s) - Werner - 06-11-2020, 05:17 AM
RE: Lambert W Function (hp-42s) - Werner - 06-11-2020, 09:20 AM
RE: Lambert W Function (hp-42s) - lyuka - 09-28-2020, 04:06 PM
RE: Lambert W Function (hp-42s) - Werner - 09-30-2020, 09:12 AM
RE: Lambert W Function (hp-42s) - Werner - 10-02-2020, 03:02 PM
RE: Lambert W Function (hp-42s) - Werner - 09-30-2020, 07:08 AM
RE: Lambert W Function (hp-42s) - lyuka - 09-29-2020, 09:21 AM
RE: Lambert W Function (hp-42s) - lyuka - 09-29-2020, 11:17 PM
RE: Lambert W Function (hp-42s) - lyuka - 09-30-2020, 11:04 AM
RE: Lambert W Function (hp-42s) - lyuka - 09-30-2020, 07:16 PM
RE: Lambert W Function (hp-42s) - Werner - 10-01-2020, 09:37 AM
RE: Lambert W Function (hp-42s) - Werner - 10-01-2020, 01:39 PM
RE: Lambert W Function (hp-42s) - lyuka - 10-01-2020, 06:25 PM
RE: Lambert W Function (hp-42s) - lyuka - 10-02-2020, 05:44 AM
RE: Lambert W Function (hp-42s) - lyuka - 10-03-2020, 07:56 PM
RE: Lambert W Function (hp-42s) - Werner - 10-05-2020, 08:03 AM
RE: Lambert W Function (hp-42s) - lyuka - 10-05-2020, 06:09 PM
RE: Lambert W Function (hp-42s) - Werner - 10-06-2020, 06:16 AM
RE: Lambert W Function (hp-42s) - lyuka - 11-09-2020, 08:30 AM



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