<html><head><meta http-equiv="Content-Type" content="text/html charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; -webkit-line-break: after-white-space; "><br><div><div>On Feb 19, 2013, at 12:53 PM, Marcelo Xavier Guterres <<a href="mailto:m.guterres@gmail.com">m.guterres@gmail.com</a>> wrote:</div><br class="Apple-interchange-newline"><blockquote type="cite"><div><div style="display:inline-block"><span></span></div></div> <div>
<div dir="ltr" style="zoom:1"><span lang="en">Esteemed colleague,<br><br></span><span lang="en"><span>thanks for the</span> <span>previous answer</span><span>. </span></span><span id="result_box" class="short_text" lang="en"><span class="hps">But</span> <span class="hps">still can not</span> <span class="hps">understand</span> <span class="hps">one aspect</span><span class="">.<br>
<br></span></span><br><span id="result_box" class="" lang="en"><span class="hps">The</span> <span class="hps">GMRES</span> <span class="hps">behaves</span> <span class="hps">well up to</span> <span class="hps">a point</span><span>,</span> <span class="hps">but then</span> <span class="hps">the quality</span> <span class="hps">of the final solution</span> <span class="hps">is bad</span><span>,</span> <span class="hps">compared to</span> <span class="hps">analytical solution</span><span>.<br>
<br><br></span></span><span id="result_box" class="short_text" lang="en"><span class="hps">It is a problem</span> <span class="hps">in the method or</span> <span class="hps">truncation error</span><span class="">?<br></span></span></div></div></blockquote><div><br></div><div>No, it is an approximate solver and it gets worse as the problem size increases. CG gets worse also. CG is just better for this problem.</div><br><blockquote type="cite"><div><div dir="ltr" style="zoom:1"><span id="result_box" class="short_text" lang="en"><span class=""><br>
<br></span></span><table cellpadding="3" cellspacing="0"><tbody><tr><td style="background:#ccffcc;font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="center" valign="bottom" bgcolor="#CCFFCC">
<i>m</i></td>
<td style="background:#ccffcc;font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="center" valign="bottom" bgcolor="#CCFFCC"><i>n</i></td>
<td style="background:#ccffcc;font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="center" valign="bottom" bgcolor="#CCFFCC"><i>m x n</i></td>
<td style="background:#ccffcc;font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="center" valign="bottom" bgcolor="#CCFFCC"><i>error ( KSPCG x PCJACOBI )</i></td>
<td colspan="3" style="background:#ccffcc;font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000;border-right:thin solid #000000" align="center" valign="bottom" bgcolor="#CCFFCC"><i>error ( KSPGMRS x PCJACOBI )</i></td>
</tr>
<tr>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">3</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">3</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">9</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">1,92E−16</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000;border-right:thin solid #000000" align="right" valign="bottom">4,42E−16</td>
<td><br></td>
<td><br></td>
</tr>
<tr>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">4</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">4</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">16</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">2,08E−16</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000;border-right:thin solid #000000" align="right" valign="bottom">6,46E−16</td>
<td><br></td>
<td><br></td>
</tr>
<tr>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">5</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">5</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">25</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">4,41E−16</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000;border-right:thin solid #000000" align="right" valign="bottom">9,63E−16</td>
<td><br></td>
<td><br></td>
</tr>
<tr>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">6</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">6</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">36</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">8,77E−16</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000;border-right:thin solid #000000" align="right" valign="bottom">8,26E−16</td>
<td><br></td>
<td><br></td>
</tr>
<tr>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">7</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">7</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">49</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">2,37E−06</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000;border-right:thin solid #000000" align="right" valign="bottom">2,52E−06</td>
<td><br></td>
<td><br></td>
</tr>
<tr>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">8</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">8</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">64</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">1,17E−05</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000;border-right:thin solid #000000" align="right" valign="bottom">1,33E−05</td>
<td><br></td>
<td><br></td>
</tr>
<tr>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">9</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">9</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">81</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">9,32E−06</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000;border-right:thin solid #000000" align="right" valign="bottom">1,26E−05</td>
<td><br></td>
<td><br></td>
</tr>
<tr>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">10</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">10</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">100</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">7,33E−06</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000;border-right:thin solid #000000" align="right" valign="bottom">9,93E−06</td>
<td><br></td>
<td><br></td>
</tr>
<tr>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">20</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">20</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">400</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">4,22E−05</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000;border-right:thin solid #000000" align="right" valign="bottom">3,16E−04</td>
<td><br></td>
<td><br></td>
</tr>
<tr>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">30</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">30</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">900</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">1,06E−04</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000;border-right:thin solid #000000" align="right" valign="bottom">2,37E−02</td>
<td><br></td>
<td><br></td>
</tr>
<tr>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">40</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">40</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">1600</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">2,14E−04</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000;border-right:thin solid #000000" align="right" valign="bottom">3,77E−02</td>
<td><br></td>
<td><br></td>
</tr>
<tr>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">50</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">50</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">2500</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">3,37E−04</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000;border-right:thin solid #000000" align="right" valign="bottom">9,36E−03</td>
<td><br></td>
<td><br></td>
</tr>
<tr>
<td style="background:#ccffcc;font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom" bgcolor="#CCFFCC">100</td>
<td style="background:#ccffcc;font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom" bgcolor="#CCFFCC">100</td>
<td style="background:#ccffcc;font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom" bgcolor="#CCFFCC">10000</td>
<td style="background:#ccffcc;font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom" bgcolor="#CCFFCC">1,27E−03</td>
<td style="background:#ccffcc;font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000;border-right:thin solid #000000" align="right" valign="bottom" bgcolor="#CCFFCC">6,53E−02</td>
<td><br></td>
<td><br></td>
</tr>
<tr>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">200</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">200</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">40000</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">4,32E−03</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000;border-right:thin solid #000000" align="right" valign="bottom">3,67E−01</td>
<td><br></td>
<td><br></td>
</tr>
<tr>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">300</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">300</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">90000</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">9,53E−02</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000;border-right:thin solid #000000" align="right" valign="bottom">1,02E+00</td>
<td><br></td>
<td><br></td>
</tr>
<tr>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">400</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">400</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">160000</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">1,68E−02</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-left:thin solid #000000;border-right:thin solid #000000" align="right" valign="bottom">2,10E+00</td>
<td><br></td>
<td><br></td>
</tr>
<tr>
<td style="font-size:10pt;border-top:thin solid #000000;border-bottom:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">500</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-bottom:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">500</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-bottom:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">250000</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-bottom:thin solid #000000;border-left:thin solid #000000" align="right" valign="bottom">2,61E−02</td>
<td style="font-size:10pt;border-top:thin solid #000000;border-bottom:thin solid #000000;border-left:thin solid #000000;border-right:thin solid #000000" align="right" valign="bottom">3,66E+00</td>
<td><br></td>
<td><br></td></tr></tbody></table><br>
</div></div><br clear="all"><br>-- <br>Saudações Pampeanas<br>-- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --<br><br>Phd. student Marcelo<br>
</blockquote></div><br></body></html>