Small Solver Program

[Thomas Klemm]

(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