<div class="gmail_quote">On Tue, Apr 3, 2012 at 14:25, RenZhengYong <span dir="ltr"><<a href="mailto:renzhengyong@gmail.com">renzhengyong@gmail.com</a>></span> wrote:<br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
<div id=":1rt">I have a question to ask for your suggestions which is to solve Ax=b using GMRES, <br>here A is partially dense. Using petsc, I successfully used the matrix-free approach to solve<br>it so that the expensive storage of A is avoided. My question is could I offer an matrix B <br>
(which is sparse matrix and good approximation to A) so that the convergence rate of <br>GMRES can be speed up. </div></blockquote></div><br><div>Certainly, but the challenge is to find this other operator. You could try sparse approximate methods to approximate either the operator or its inverse. Other approaches would typically involve further knowledge of your problem.</div>