Question

I needed an application for solving linear systems of equations (N up to 10), so I got different codes, and compile them, and they seem to work, but I get lots of problems with precision. I mean, the solvers are really very sensitive to small changes of the system.

So, could somebody recommend to me a reliable commandl ine application for this purpose? Or some useful open source code (and easy to compile)

Thanks

Answer 1

GNU Octave is essentially a free version of Matlab (the syntax is identical for basic operations), so you can try things out there and see how they compare to the answers that you’re getting.

Having said that, if your answer is very sensitive to the input, it’s possible that your problem is ill-conditioned – you can check this by computing the condition number of the matrix in Octave. It’s hard to say what to do in that case without knowing more specifics on the problem.

Also, you don’t mention which method you’re currently using. Gaussian elimination (i.e. “what you learned in math class”) is notoriously numerically unstable if you don’t use pivoting (see the wikipedia entry for “Pivoting”); adding that might be enough to improve the quality of the results.