Most impressive/complex/amazing C-series program?

[Thomas Klemm]

(08-11-2018 12:28 PM)Albert Chan Wrote:  Just a comment of using linear regression to solve linear problems.

Not sure if that was not made clear but we're not using the linear regression the way described in your example.
Instead we use the internal algorithm used to solve the linear equations that appear in the context of linear regression with values completely unrelated to that subject.

The internal 13 digit accuracy allows to solve equations where a naïve approach (e.g. by using explicit formulas) would fail due to cancellation.

Example:

\(\begin{bmatrix}
1000001&1000000\\
1000000&999999
\end{bmatrix}
\begin{bmatrix}
x\\
y
\end{bmatrix}
=
\begin{bmatrix}
3000002\\
2999999
\end{bmatrix}\)

The determinant \(1000001\times999999-1000000^2\) turns out to be \(0\) on the HP-11C.

However you can still solve the system by entering:

CLEAR ∑
999999
STO 0
1000000
STO 1
1000001
STO 2
2999999
STO 3
3000002
STO 5
L.R.

Y: 2
X: 1

Thus the solutions are \(x=2, y=1\).

Kind regards
Thomas