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Hi Mark,</div>
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Thanks for your reply. Below is the output if I call KSPComputeEigenvalues<br>
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0.330475 -0.0485014
<div class="ContentPasted0">0.521211 0.417409</div>
<div class="ContentPasted0">0.684726 -0.377126</div>
<div class="ContentPasted0">0.885941 0.354342</div>
<div class="ContentPasted0">0.957845 -0.0508471</div>
<div class="ContentPasted0">0.964676 -0.241642</div>
<div class="ContentPasted0">1.05921 0.0742963</div>
1.82065 -0.0209096<br>
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I have the following questions:</div>
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<li class="ContentPasted2">These eigenvalues are sorted according to the magnitudes. so "lowest" means smallest magnitude and "highest" means largest magnitude in your previous email?</li><li class="ContentPasted2 ContentPasted3">I understand that if the preconditioner is perfect, all the eigenvalues should be (1,0). Since my preconditioner is not perfect, to understand its performance, is it correct to say that, I need to keep an eye on the
eigenvalues whose distance to (1,0) are the furthest? <br>
</li><li class="ContentPasted2 ContentPasted3 ContentPasted4">How does petsc decides how many eigenvalues to output in KSPComputeEigenvalues. I am solving a set of linear systems, sometimes KSPComputeEigenvalues outputs 8 eigenvalues, sometimes it outputs just 2
eigenvalues. <br>
</li><li class="ContentPasted2 ContentPasted3 ContentPasted4">In the output which I showed above, are these the ones with the smallest magnitude and also the ones with the largest magnitudes? and what's between are all ignored? If this is the case, which ones are
the "lowest" and which ones are the "highest"?<br>
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<div>Thanks for your help and sorry for so many questions,</div>
<div>Feng<br>
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<div id="divRplyFwdMsg" dir="ltr"><font style="font-size:11pt" face="Calibri, sans-serif" color="#000000"><b>From:</b> Mark Adams <mfadams@lbl.gov><br>
<b>Sent:</b> 04 October 2022 17:18<br>
<b>To:</b> feng wang <snailsoar@hotmail.com><br>
<b>Cc:</b> petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov><br>
<b>Subject:</b> Re: [petsc-users] clarification on extreme eigenvalues from KSPComputeEigenvalues</font>
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<div dir="ltr">The extreme eigenvalues are the lowest and highest.
<div>A perfect preconditioner would give all eigenvalues = 1.0</div>
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<div>Mark</div>
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<div dir="ltr" class="x_gmail_attr">On Tue, Oct 4, 2022 at 1:03 PM feng wang <<a href="mailto:snailsoar@hotmail.com" data-auth="NotApplicable">snailsoar@hotmail.com</a>> wrote:<br>
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Dear All,</div>
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I am using the KSPComputeEigenvalues to understand the performance of my preconditioner, and I am using the right-preconditioned GMRES with ASM. In the user guide, it says this routine computes the extreme eigenvalues of the preconditioned operator. If I understand
it correctly, these eigenvalues are the ones furthest away from (1,0)? If the preconditioning is perfect, all the eigenvalues should be (1,0).<br>
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Thanks,</div>
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Feng<br>
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