Small Solver Program
02-15-2019, 06:26 PM
Post: #5
 Thomas Klemm Senior Member Posts: 1,851 Joined: Dec 2013
RE: Small Solver Program
(02-15-2019 12:07 AM)Albert Chan Wrote:  It would be nice if we can temper the oscillation, or slow convergence.

We can also use Aitken's delta-squared process to accelerate the speed of convergence:

$$a_{n}=x_{n+2}-\frac {(x_{n+2}-x_{n+1})^{2}}{(x_{n+2}-x_{n+1})-(x_{n+1}-x_{n})}$$

This leads to the following program for the HP-11C:
Code:
001-42,21, 1 :    ▸LBL 01 002-      36 :     ENTER 003-    32 0 :     GSB 00 004-      30 :     - 005-  43  36 :     LSTx 006-      36 :     ENTER 007-    32 0 :     GSB 00 008-      30 :     - 009-  43  36 :     LSTx 010-      34 :     x<>y 011-  43  33 :     R↑ 012-      34 :     x<>y 013-      30 :     - 014-  43  36 :     LSTx 015-  43  11 :     x² 016-      34 :     x<>y 017-      10 :     ÷ 018-      30 :     - 019-  43  32 :     RTN 020-42,21, 0 :    ▸LBL 00 021-  43  12 :     LN 022-    45 0 :     RCL 00 023-      34 :     x<>y 024-      10 :     ÷ 025-  43  32 :     RTN

Example:

Solve: $$x^x=1000$$

1000 LN
STO 0

4.6
GSB 1
4.555665779
R/S
4.555535706
R/S
4.555535705
R/S
Error 0

Feel free to add a check for 0 after line 13 to prevent the error and loop back to label 1 instead of returning in line 19.

Cheers
Thomas
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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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