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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>
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    <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>
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      <br>
      -------- Forwarded Message --------
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            <th align="RIGHT" valign="BASELINE" nowrap="nowrap">Subject:
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            <td>[CSC 435] Matrices</td>
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            <th align="RIGHT" valign="BASELINE" nowrap="nowrap">Resent-From:
            </th>
            <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">&lt;POUNDS_AJ@mercer.edu&gt;</a></td>
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            <th align="RIGHT" valign="BASELINE" nowrap="nowrap">Reply-To:
            </th>
            <td>Andrew J. Pounds <a class="moz-txt-link-rfc2396E" href="mailto:POUNDS_AJ@mercer.edu">&lt;POUNDS_AJ@mercer.edu&gt;</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">&lt;csc435@theochem.mercer.edu&gt;</a></td>
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      <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>
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      <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>
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      <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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