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Oct 10, 2012 at 18:19 comment added David Ketcheson I recommend asking this question on scicomp.stackexchange.com.
Sep 21, 2012 at 19:09 comment added Andrew T. Barker How large is your system? Where does it come from? I don't understand your second paragraph; if $ \epsilon = 0 $ don't you just have a diagonal matrix? Since $ D + \epsilon S $ is a small perturbation of a diagonal matrix, I would expect a very simple scheme like Jacobi or Gauss-Seidel to converge fairly quickly. To be a little more sophisticated you could try diagonally preconditioned GMRES. Finally, you might get more answers at scicomp.stackexchange.com
Sep 21, 2012 at 14:50 history asked Nat Trask CC BY-SA 3.0