I am currently working on a C++-based library for large, sparse linear algebra problems (yes, I know many such libraries exist, but I'm rolling my own mostly to learn about iterative solvers, sparse storage containers, etc..).
I am to the point where I am using my solvers within other programming projects of mine, and would like to test the solvers against problems that are not my own. Primarily, I am looking to test against symmetric sparse systems that are positive definite. I have found several sources for such system matrices such as:
Matrix Market UF Sparse Matrix Collection
That being said, I have not yet found any sources of good test matrices that include the entire system- system matrix and RHS. This would be great to have in order to check results. Any tips on where I can find such full systems, or alternatively, what I might do to generate a "good" RHS for the system matrices I can get online? I am currently just filling a matrix with random values, or all ones, but suspect that this is not necessarily the best way.