I am looking for a C library to solve linear and, if possible, nonlinear matrix equation of the form Ax = b. It is important to me, that the packages are not too big and free of charge. Speed does not matter as much as simplicity and the sparse feature of the matrix storage. Also, it should be able to parallelize the calculations. Since I am fairly new in the blas/lapack/… field of numerical linear algebra, it would be great if it contained a nice documentation, possibly with examples. Are there any packages you can recommend? I am a bit overwhelmed by the google results and also don’t know the names of the routines I would have to look for.
I just found SuperLu which seems to have a very nice documentation, even with code snippets. It is written in C and requires CBLAS.
You have a lot of different options. Before you start, you should consider some guidelines for choosing a sparse linear solver. I personally recommend PETSc, but see this curated list over on scicomp for a more comprehensive list of options.