I need to programmatically solve a system of linear equations in C, Objective C, or (if needed) C++.
Here's an example of the equations:
-44.3940 = a * 50.0 + b * 37.0 + tx
-45.3049 = a * 43.0 + b * 39.0 + tx
-44.9594 = a * 52.0 + b * 41.0 + tx
From this, I'd like to get the best approximation for a
, b
, and tx
.
Cramer's Rule and Gaussian Elimination are two good, general-purpose algorithms (also see Simultaneous Linear Equations). If you're looking for code, check out GiNaC, Maxima, and SymbolicC++ (depending on your licensing requirements, of course).
EDIT: I know you're working in C land, but I also have to put in a good word for SymPy (a computer algebra system in Python). You can learn a lot from its algorithms (if you can read a bit of python). Also, it's under the new BSD license, while most of the free math packages are GPL.