I will have to solve a large linear system. I'm now looking for a solver that works "matrix-free" (So that I just have to specify a matrix-vector product, but not the matrix). As far as I understand (I'm not an expert.) LAPACK does not provide this option.
Can you recommend any libraries? Or is my approach to implement this matrix-free not reasonable at all?
Remark: I plan to use C++ and the matrix comes up from a FEM for a system of PDEs, but is not symmetric. The matrix is sparse, but as I plan to provide the matrix-vector product by myself, and the resulting vector will be dense, sparsity should not play a role here - as far as I understand.