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The earlier e-mail I sent you about building diagonally dominant
matrices apparently does not go far enough. Change the line<br>
<br>
<font face="Courier New, Courier, monospace">matrixa(j,i) = 2.0 *
ranval * DIM<br>
<br>
to <br>
<br>
</font><br>
<font face="Courier New, Courier, monospace">matrixa(j,i) = ranval
* DIM * DIM<br>
<br>
<br>
to guarantee that the matrix will be diagonally dominant. Again,
this should only be a problem when it comes to the iterative
linear solver.<br>
</font>
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-------- Forwarded Message --------
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<th align="RIGHT" valign="BASELINE" nowrap="nowrap">Subject:
</th>
<td>[CSC 435] Matrices</td>
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<th align="RIGHT" valign="BASELINE" nowrap="nowrap">Resent-From:
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<td><a class="moz-txt-link-abbreviated" href="mailto:pounds_aj@mercer.edu">pounds_aj@mercer.edu</a></td>
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<th align="RIGHT" valign="BASELINE" nowrap="nowrap">Date: </th>
<td>Wed, 23 Mar 2016 18:43:46 +0000</td>
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<th align="RIGHT" valign="BASELINE" nowrap="nowrap">From: </th>
<td>Andrew J. Pounds <a class="moz-txt-link-rfc2396E" href="mailto:POUNDS_AJ@mercer.edu"><POUNDS_AJ@mercer.edu></a></td>
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<th align="RIGHT" valign="BASELINE" nowrap="nowrap">Reply-To:
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<td>Andrew J. Pounds <a class="moz-txt-link-rfc2396E" href="mailto:POUNDS_AJ@mercer.edu"><POUNDS_AJ@mercer.edu></a></td>
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<th align="RIGHT" valign="BASELINE" nowrap="nowrap">To: </th>
<td><a class="moz-txt-link-abbreviated" href="mailto:csc435@theochem.mercer.edu">csc435@theochem.mercer.edu</a>
<a class="moz-txt-link-rfc2396E" href="mailto:csc435@theochem.mercer.edu"><csc435@theochem.mercer.edu></a></td>
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charset=windows-1252">
<font face="serif">Guys -- while the direct linear solver does not
have to have a diagonally dominant matrix to guarantee
convergence (it does the row interchanges to obviate the need
for that requirement) the iterative linear solver needs to have
a diagonally dominant matrix "A" to <i>guarantee</i>
convergence. <br>
<br>
Here is how I constructed my matrix A in my Fortran code to make
sure I was close to diagonal dominance.<br>
<br>
</font><br>
<font face="Courier New, Courier, monospace">do i = 1, DIM <br>
do j = 1, DIM <br>
call random_number(ranval)<br>
if ( i .ne. j) then<br>
matrixa(j,i) = ranval <br>
else<br>
matrixa(j,i) = 2.0 * ranval * DIM<br>
endif<br>
enddo<br>
enddo</font><br>
<font face="serif"><br>
<br>
</font>
<pre class="moz-signature" cols="72">--
Andrew J. Pounds, Ph.D. (<a moz-do-not-send="true" class="moz-txt-link-abbreviated" href="mailto:pounds_aj@mercer.edu">pounds_aj@mercer.edu</a>)
Professor of Chemistry and Computer Science
Mercer University, Macon, GA 31207 (478) 301-5627
<a moz-do-not-send="true" class="moz-txt-link-freetext" href="http://faculty.mercer.edu/pounds_aj">http://faculty.mercer.edu/pounds_aj</a>
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