title: Looking for testing matrices/systems for iterative linear solver
body: <p>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..).</p>
  
  <p>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:</p>
  
  <p><a href="http://math.nist.gov/MatrixMarket/" rel="noreferrer">Matrix Market</a>
  <a href="http://www2.research.att.com/~yifanhu/GALLERY/GRAPHS/search.html" rel="noreferrer">UF Sparse Matrix Collection</a></p>
  
  <p>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.</p>