<div style="line-height:1.7;color:#000000;font-size:14px;font-family:arial"><DIV><BR>I am sorry.</DIV>
<DIV>In my view, preconditioned resid norm:||rp||=||Bb-BAx||(B is the preconditioned matrix);<BR>true resid norm:||rt||=||b-Ax||; ||r(i)||/||b||: ||rt||/||b||. Is it right?</DIV>
<DIV>(1) Divergence is detected if <BR> <BR> ||rp||/||b|| > dtol or ||rt||/||b|| > dtol ?</DIV>
<DIV> Both of them (rt/b:1.701448294063e+04 / 6.7139E+4; rt/b:2.716078947576e+04; dtol=1.0E+5 )</DIV>
<DIV>are not in this example, but it is divergent?</DIV>
<DIV><BR>(2) Convergence is detected at iteration k if :</DIV>
<DIV> ||rp||/||b|| < rtol </DIV>
<DIV> But I find that when "preconditioned resid norm" is less than rtol, it begins to be convergent(another example,rtol=1.0E-15):</DIV>
<DIV>19 KSP preconditioned resid norm 4.964358598559e-15 true resid norm 1.076736705942e-08 ||r(i)||/||b|| 1.603737473724e-13<BR>120 KSP preconditioned resid norm 1.045516340849e-14 true resid norm 1.089531944048e-08 ||r(i)||/||b|| 1.622795245901e-13<BR>121 KSP preconditioned resid norm 1.209016864072e-14 true resid norm 1.096191254361e-08 ||r(i)||/||b|| 1.632713906089e-13<BR>122 KSP preconditioned resid norm 1.568004225873e-15 true resid norm 1.073893120243e-08 ||r(i)||/||b|| 1.599502116167e-13<BR>123 KSP preconditioned resid norm 5.066448468788e-15 true resid norm 1.078375214589e-08 ||r(i)||/||b|| 1.606177938235e-13<BR>124 KSP preconditioned resid norm 3.619818305395e-16 true resid norm 1.073887987132e-08 ||r(i)||/||b|| 1.599494470692e-13<BR>Linear solve converged due to CONVERGED_RTOL iterations 124</DIV>
<DIV> In iteration 124, preconditioned resid norm begins to be smaller than rtol.</DIV>
<DIV><BR> Thanks. Jim<BR><BR><BR><BR></DIV>
<DIV></DIV>
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<DIV><BR></DIV>>On 2013-01-09 01:13:44£¬"Jed Brown" <jedbrown@mcs.anl.gov> дµÀ£º<BR>
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<DIV class="gmail_extra">>>On Tue, Jan 8, 2013 at 11:08 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>>>354 KSP preconditioned resid norm 2.882557881065e-01 true resid norm 3.089426814670e+04 ||r(i)||/||b|| 4.601523777979e-01<BR></DIV></BLOCKQUOTE>
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<DIV>>^^ Notice how this ratio is less than 1.0? DTOL is defined in terms of the smallest residual norm seen.</DIV>
<DIV> </DIV>
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<DIV>>>355 KSP preconditioned resid norm 2.170676916299e+02 true resid norm 2.326457175403e+07 ||r(i)||/||b|| 3.465124326697e+02<BR>>>356 KSP preconditioned resid norm 5.764266225925e+00 true resid norm 6.177943120636e+05 ||r(i)||/||b|| 9.20169 1405543e+00<BR>>>357 KSP preconditioned resid norm 1.701448294063e+04 true resid norm 1.823554008687e+09 ||r(i)||/||b|| 2.716078947576e+04
<DIV class="im"><BR>>>Linear solve did not converge due to DIVERGED_DTOL iterations 357</DIV></DIV>
<DIV> </DIV>
<DIV>>>I cannot understand it. Which one means that the DIVERGED_DTOL occures:preconditioned resid norm, true resid norm or ||r(i)||/||b||?</DIV>
<DIV>>>What is the difference between preconditioned resid norm and true resid norm?</DIV></BLOCKQUOTE></DIV><BR></DIV>
<DIV class="gmail_extra">>It uses the norm that your method is running. In this case, it's the preconditioned norm.</DIV></DIV></BLOCKQUOTE></div><br><br><span title="neteasefooter"><span id="netease_mail_footer"></span></span>