On Tue, Aug 7, 2012 at 9:55 AM, w_ang_temp <span dir="ltr"><<a href="mailto:w_ang_temp@163.com" target="_blank">w_ang_temp@163.com</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">
<div style="line-height:1.7;font-size:14px;font-family:arial"><div>Hello,</div>
<div> I am sorry that I cannot understand "Make sure to avoid restarts". In the FAQ, it says that using the restarted</div>
<div>GMRES method to get approximations to the condition number. So why saying "avoid restarts" in the next following?</div></div></blockquote><div><br></div><div>Jim, in order to understand this, it is necessary to understand GMRES. Please read the section in Yousef Saad's book. We</div>
<div>are factoring the Hessenberg matrix it produces to get estimates. If you restart, that is thrown away.</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">
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<div> Besides, there are two questions about GMRES:</div>
<div> (1) Is the "iterations count" of GMRES with restarted parameters which is outputted by PETSc meaningless?</div>
<div> (2) Is there only restarted GMRES in PETSc?</div>
<div> Thanks.</div>
<div> Jim<br><br></div>
<div></div>
<div></div>
<div><br></div>>>在 2012-08-07 21:59:05，"Matthew Knepley" <<a href="mailto:knepley@gmail.com" target="_blank">knepley@gmail.com</a>> 写道：<br>
<blockquote style="BORDER-LEFT:#ccc 1px solid;MARGIN:0px 0px 0px 0.8ex;PADDING-LEFT:1ex">>>On Tue, Aug 7, 2012 at 8:56 AM, w_ang_temp <span dir="ltr"><<a href="mailto:w_ang_temp@163.com" target="_blank">w_ang_temp@163.com</a>></span> wrote:<br>
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<div><br>>>Hello, Jed</div>
<div>>> I am a little puzzled about the "How can I determine the condition number of a matrix?" in the</div>
<div>>>FAQ. The details are as follows:<br> <br>>> "...For larger matrices, you can run with <em>-pc_type none -ksp_type gmres -ksp_monitor_singular_value </em></div>
<div>>><em>-ksp_gmres_restart 1000</em> to get approximations to the condition number of the operator. This will </div>
<div>>>generally be accurate for the largest singular values, but may overestimate the smallest singular </div>
<div>>>value unless the method has converged. Make sure to avoid restarts...".<br> <br>>> Since the command "<em>-pc_type none -ksp_type gmres -ksp_monitor_singular_value</em> </div>
<div>>><em>-ksp_gmres_restart 1000</em>" using restart parameter, so, what does "Make sure to avoid restarts" mean?</div></div></blockquote>
<div><br></div>
<div>>Do not believe the answer after the restart.</div>
<div> </div>
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<div>>>Besides, is the parameter "<em>1000</em>" a reference value which will be changed in specific project in order</div>
<div>>>to be converged? Or must use <em>1000 </em>to get the condition number?</div></div></blockquote>
<div><br></div>
<div>>The former.</div>
<div><br></div>
<div> > Matt</div>
<div> </div>
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<div> >> Thanks.</div>
<div> >> Jim</div></div></blockquote></div></blockquote></div><br><br><span title="neteasefooter"><span></span></span></blockquote></div><br><br clear="all"><div>
<br></div>-- <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>