Small Solver Program
02-15-2019, 12:07 AM (This post was last modified: 11-10-2019 03:03 PM by Albert Chan.)
Post: #4
 Albert Chan Senior Member Posts: 2,551 Joined: Jul 2018
RE: Small Solver Program
(02-14-2019 07:06 AM)Thomas Klemm Wrote:  $$x=\frac{3}{LOG(x)}$$

4
R/S
4.982892143
R/S
4.301189432
...

It would be nice if we can temper the oscillation, or slow convergence.
Let x0 = 4, x1, x2 = the first two iterated values.

Rate = (x2-x1)/(x1-x0) ≈ (4.30 - 4.98) / (4.98 - 4) = -0.694

If the same trend continued, we expect final % = 1/(1-r) ~ 60%

x ≈ x0/(1-r) = (x1 - (x1-x0))/(1-r) = (x1 - r x0) / (1-r)

Use weighted fixed-point equation x = 0.6 * 3/log10(x) + 0.4 x

4.6
4.555924149
4.555537395
4.555535712
4.555535705 (converged)

Edit: compare with Newton's method, x = (ln(1000) + x) / (ln(x) + 1)
4
4.571001573
4.555546101
4.555535705 (converged)
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 Messages In This Thread Small Solver Program - Gamo - 02-14-2019, 05:25 AM RE: Small Solver Program - Thomas Klemm - 02-14-2019, 07:06 AM RE: Small Solver Program - Albert Chan - 02-15-2019 12:07 AM RE: Small Solver Program - Thomas Klemm - 02-15-2019, 06:26 PM RE: Small Solver Program - Albert Chan - 02-15-2019, 09:16 PM Addendum: Small Solver Program - Thomas Klemm - 02-14-2019, 07:15 AM RE: Small Solver Program - Thomas Klemm - 02-16-2019, 03:58 AM RE: Small Solver Program - Albert Chan - 11-03-2019, 03:14 PM RE: Small Solver Program - Albert Chan - 11-10-2019, 07:02 PM RE: Small Solver Program - Albert Chan - 12-01-2019, 12:13 AM RE: Small Solver Program - Csaba Tizedes - 02-16-2019, 12:24 PM RE: Small Solver Program - Thomas Klemm - 02-16-2019, 01:42 PM RE: Small Solver Program - Csaba Tizedes - 02-16-2019, 03:24 PM RE: Small Solver Program - Gamo - 02-17-2019, 02:57 AM RE: Small Solver Program - Thomas Klemm - 02-17-2019, 09:06 AM RE: Small Solver Program - Gamo - 02-17-2019, 02:33 PM RE: Small Solver Program - Thomas Klemm - 02-17-2019, 04:57 PM RE: Small Solver Program - Gamo - 02-18-2019, 03:49 AM RE: Small Solver Program - Thomas Klemm - 02-18-2019, 05:20 AM RE: Small Solver Program - Dieter - 02-18-2019, 07:46 PM RE: Small Solver Program - Thomas Klemm - 02-18-2019, 10:22 PM RE: Small Solver Program - Albert Chan - 02-19-2019, 01:10 AM RE: Small Solver Program - Csaba Tizedes - 02-19-2019, 08:39 AM RE: Small Solver Program - Thomas Klemm - 02-20-2019, 05:31 AM RE: Small Solver Program - Csaba Tizedes - 02-25-2019, 08:39 PM RE: Small Solver Program - Thomas Klemm - 02-20-2019, 07:22 AM RE: Small Solver Program - Thomas Klemm - 02-24-2019, 09:21 AM RE: Small Solver Program - Thomas Klemm - 02-25-2019, 11:00 PM RE: Small Solver Program - Albert Chan - 01-04-2020, 07:49 PM

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