Most impressive/complex/amazing C-series program?

[Thomas Klemm]

The HP-11C can solve a linear, symmetric 2×2 system using the built-in linear regression with a single operation:

Code:

L.R.

For this to work we have to fill the registers R₀ - R₅ with the corresponding values of the equation:

\(\begin{bmatrix}
R_2 & R_1 \\
R_1 & R_0
\end{bmatrix}\cdot\begin{bmatrix}
Y \\
X
\end{bmatrix}=\begin{bmatrix}
R_5 \\
R_3
\end{bmatrix}\)

Example:

\(\begin{bmatrix}
2 & -3 \\
-3 & 5
\end{bmatrix}\cdot\begin{bmatrix}
2 \\
-3
\end{bmatrix}=\begin{bmatrix}
13 \\
-21
\end{bmatrix}\)

CLEAR Σ
2 STO 2
-3 STO 1
5 STO 0
13 STO 5
-21 STO 3
L.R.

Y: 2
X: -3


This is used in Bairstow's Method.

Kind regards
Thomas

BTW: Not all models allow this trick as they check the values for consistency prior to calculating the result. E.g. the value of n in register R₀ can't be negative.