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<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Victor,<o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>I am wondering if you have any plan to implement Induced
Dimension Reduction (IDR(s) by Sonneveld and van Gijzen) in PETSc. <o:p></o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'><o:p> </o:p></span></p>
<p class=MsoNormal><span style='font-size:11.0pt;font-family:"Calibri","sans-serif";
color:#1F497D'>Thanks,<o:p></o:p></span></p>
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<p class=MsoNormal><span style='font-size:10.0pt;font-family:"Arial","sans-serif";
color:#1F497D'>================================<br>
Keita Teranishi<br>
Scientific Library Group<br>
Cray, Inc.<br>
keita@cray.com<br>
================================</span><span style='font-size:11.0pt;
font-family:"Calibri","sans-serif";color:#1F497D'><o:p></o:p></span></p>
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<p class=MsoNormal><b><span style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>From:</span></b><span
style='font-size:10.0pt;font-family:"Tahoma","sans-serif"'>
petsc-dev-bounces@mcs.anl.gov [mailto:petsc-dev-bounces@mcs.anl.gov] <b>On
Behalf Of </b>Victor Eijkhout<br>
<b>Sent:</b> Thursday, April 22, 2010 2:33 PM<br>
<b>To:</b> For users of the development version of PETSc<br>
<b>Subject:</b> Re: [petsc-dev] Yet more KSPs<o:p></o:p></span></p>
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<p class=MsoNormal>On 2010/04/12, at 1:28 AM, Matthew Knepley wrote:<o:p></o:p></p>
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<o:p></o:p></p>
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<p class=MsoNormal>Someone has gone the extra mile and made an A-orthogonal
Lanczos<o:p></o:p></p>
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<p class=MsoNormal><o:p> </o:p></p>
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<p class=MsoNormal> <a href="http://arxiv.org/pdf/1004.1622v1">http://arxiv.org/pdf/1004.1622v1</a><o:p></o:p></p>
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<p class=MsoNormal>Is that hard? Basically a slightly different inner product.
A-orthogonalization gives L2 minimal residuals. (Under the ordinary inner
product the residuals are minimal in the A^{-1} norm)<o:p></o:p></p>
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<o:p></o:p></p>
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<p class=MsoNormal>It appears to outperform BiCGStab in enough of their tests<o:p></o:p></p>
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<p class=MsoNormal><o:p> </o:p></p>
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<p class=MsoNormal>That might be true since BiCGS is based on the ordinary
Lanczos / BiCG.<o:p></o:p></p>
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<p class=MsoNormal><o:p> </o:p></p>
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<p class=MsoNormal>Hm. Why not do an A-orthogonal BicGstab. Hold on. Let me
grab some scrap paper.....<o:p></o:p></p>
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<p class=MsoNormal><o:p> </o:p></p>
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<p class=MsoNormal>Victor.<o:p></o:p></p>
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<o:p></o:p></p>
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<p class=MsoNormal><span style='font-size:9.0pt;font-family:"Helvetica","sans-serif";
color:black'>-- <o:p></o:p></span></p>
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<p class=MsoNormal><span style='font-size:9.0pt;font-family:"Helvetica","sans-serif";
color:black'>Victor Eijkhout -- 865 974 9308<o:p></o:p></span></p>
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<p class=MsoNormal><span style='font-size:9.0pt;font-family:"Helvetica","sans-serif";
color:black'>eijkhout@cs.utk.edu <a href="http://www.cs.utk.edu/~eijkhout/">http://www.cs.utk.edu/~eijkhout/</a><o:p></o:p></span></p>
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