We have a problem that leads to a system of linear equations which has to be solved numerically. There are thousands of algorithms to solve linear equations, but I haven't found any that fits our special requirements.
I've tried to describe these requirements in the pdf linked below: http://pdfcast.org/pdf/linalgproblem (Document has three pages)
Since our problem is probably a common one, we believe that there are algorithms specially designed for the kind of matrices we are facing.
Do you know someone who had the same problem? Do you know a fitting algorithm? Do you know an implementation in c++? That would help us a lot!
PS: The matrices to solve will have about 1000-10000 rows and 5000-20000 lines.
EDIT: I still hope to hear about a more specific recommendation than to use an algorithm for sparse matrices. I believe I'm not the first one having to solve this problem.