title: Using PETSc to efficiently solve a small system sequentially?
body: <p>I require solving a large set of (independent) <em>Ax</em>=<em>b</em> linear problems.
  This cannot be parallelized (or more specifically, this is within each processor's responsibility anyway).</p>
  
  <p>The <em>Ax</em>=<em>b</em> sets are small (say 10x10 at most) but are dense (Usually all terms are non-zero) and both A matrices and RHS vectors are completely different and independent.</p>
  
  <p>What is the most efficient/practical way of solving a large set of small Ax=b problems using PETSc?</p>
  
  <p>I.e. how costly would it be to have a single <em>A</em> matrix and a single <em>b</em> vector to be modified all the time and solved for each system?</p>