Small Solver Program
01-04-2020, 07:49 PM
Post: #29
 Albert Chan Senior Member Posts: 2,230 Joined: Jul 2018
RE: Small Solver Program
Just realized rate formula is equivalent to secant's method !

Post #6 showed rate formula is equivalent to Aitken's formula.
Post #27 showed we can visualize sequence running backwards, getting the same formula.

Assuming iteration formula f, with b = f(a), c = f(b):

$$Aitken(a,b,c) = Aitken(c,b,a) = a - {(a-b)^2 \over (a-b)-(b-c)}$$

If we make 2 points: $$(x_1,y_1) = (a,a-b) \;,\; (x_2, y_2) = (b,b-c)$$, we have:

$$Aitken(a,b,c) = x_1 - y_1 \left({x_1 - x_2 \over y_1 - y_2}\right)$$

This is the formula for secant's method, interpolate for y = x - f(x) = 0

QED
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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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