On Tue, Mar 1, 2011 at 2:45 PM, Umut Tabak <span dir="ltr"><<a href="mailto:u.tabak@tudelft.nl">u.tabak@tudelft.nl</a>></span> wrote:<br><div class="gmail_quote"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
Dear list,<br>
<br>
While testing an ill-conditioned system solution with minres and gmres(default 30 restarts, and no other options) in PETSc, I came up with the result that the system is solved in 155 iterations by minres to a relative default tolerance but it could not be solved by gmres.<br>
<br>
The original system is indefinite and had a condition number on the order of 10e+6, with a diagonal conditioning left and right, I could lower the condition number to the order of 10e+4 (however still indefinite with negative eigenvalues) and try to solve this system. On the other hand, I am also trying to understand the details of minres and gmres, so they both minimize the 2 norm of residual by solving a least squares problem where the latter is for unsymmetric systems, and the other is using a 3-term recurrence relation similar to cg (which I am trying to figure out now.). I would expect both to give the same result in PETSc however gmres fails. I wanted to check also gmres because I read in<br>
<br>
"Iterative Krylov Methods for Large Linear Systems" van der Vorst, Chap.6 Gmres and Minres, page 86<br>
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where it is mentioned that gmres could be more robust and less vulnerable to rounding errors than minres.<br></blockquote><div><br></div><div>Henk did not count on different orhogonalization strategies. Try -ksp_gmres_modifiedgramschmidt</div>
<div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
What could be the reason for this? Any comments are appreciated<br>
<br>
Best,<br><font color="#888888">
Umut<br>
</font></blockquote></div><br><br clear="all"><br>-- <br>What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.<br>-- Norbert Wiener<br>