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<html xmlns="http://www.w3.org/1999/xhtml" xml:space="preserve"><head><title>C Library, Mark 7 : f01 Chapter Contents</title><link rel="stylesheet" href="../styles/libdoc.css" type="text/css"/></head><body bgcolor="#FFFFFF"><hr/><div><a href="f01_intro.xml">Chapter Introduction</a></div><div><a href="../mark7.xml">NAG C Library Contents</a></div><hr/><img src="../images/topbar/title_numeric_cl.gif" alt="NAG C Library" hspace="0" width="506" height="117" border="0"/>
   <h2><a name="f01"/>f01 &#8211; Matrix Factorizations</h2>
         <div class="paramtext">
            <a class="secref" href="../F01/f01_intro.xml">f01</a> Chapter Introduction
         </div>
         <div><table class="contents">
               
               
               
               <tbody>
                  <tr>
                     <td class="contents" align="left" valign="top">
                        <b>Routine<br/>Name</b>
                     </td>
                     <td class="contents" align="left" valign="top">
                        <b>Mark of<br/>Introduction</b>
                     </td>
                     <td class="contents" align="left" valign="top">
                        <b>
                           <br/>Purpose</b>
                     </td>
                  </tr>
                  <tr>
                     <td class="contents" align="left" valign="top">
                        <a class="rtnref" href="../F01/f01bnc.xml">f01bnc</a>
                        <br/><a class="tocexample" href="../../examples/source/f01bnce.c">Example&#160;Text</a>
                        <br/><a class="tocexample" href="../../examples/data/f01bnce.d">Example&#160;Data</a>
                     </td>
                     <td class="contents" align="left" valign="top">1</td>
                     <td class="contents" align="left" valign="top">
                        <a class="rtnref" href="../F01/f01bnc.xml">nag_complex_cholesky</a>
                        <br/>
                        <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:dsi="http://www.w3.org/1999/xlink">
                           <mi>U</mi>
                           <msup>
                              <mi>U</mi>
                              <mi>H</mi>
                           </msup>
                        </math>&#160;
                        <span class="keyword">factorization</span> of <span class="keyword">complex</span> 
                        <span class="keyword">Hermitian</span> positive-<span class="keyword">definite</span> matrix</td>
                  </tr>
                  <tr>
                     <td class="contents" align="left" valign="top">
                        <a class="rtnref" href="../F01/f01mcc.xml">f01mcc</a>
                        <br/><a class="tocexample" href="../../examples/source/f01mcce.c">Example&#160;Text</a>
                        <br/><a class="tocexample" href="../../examples/data/f01mcce.d">Example&#160;Data</a>
                     </td>
                     <td class="contents" align="left" valign="top">1</td>
                     <td class="contents" align="left" valign="top">
                        <a class="rtnref" href="../F01/f01mcc.xml">nag_real_cholesky_skyline</a>
                        <br/>
                        <span class="keyword">
                           <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:dsi="http://www.w3.org/1999/xlink">
                              <mi>L</mi>
                              <mi>D</mi>
                              <msup><mi>L</mi><mi mathvariant="italic">T</mi></msup>
                           </math>&#160;                        </span> 
                        <span class="keyword">factorization</span> of real <span class="keyword">symmetric</span> positive-<span class="keyword">definite</span> 
                        <span class="keyword">variable-bandwidth</span> (skyline) matrix</td>
                  </tr>
                  <tr>
                     <td class="contents" align="left" valign="top">
                        <a class="rtnref" href="../F01/f01qcc.xml">f01qcc</a>
                        <br/><a class="tocexample" href="../../examples/source/f01qcce.c">Example&#160;Text</a>
                        <br/><a class="tocexample" href="../../examples/data/f01qcce.d">Example&#160;Data</a>
                     </td>
                     <td class="contents" align="left" valign="top">1</td>
                     <td class="contents" align="left" valign="top">
                        <a class="rtnref" href="../F01/f01qcc.xml">nag_real_qr</a>
                        <br/>
                        <span class="keyword">
                           <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:dsi="http://www.w3.org/1999/xlink">
                              <mi>Q</mi>
                              <mi>R</mi>
                           </math>&#160;                        </span> 
                        <span class="keyword">factorization</span> of real <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:dsi="http://www.w3.org/1999/xlink">
                           <mi>m</mi>
                        </math>&#160;by <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:dsi="http://www.w3.org/1999/xlink">
                           <mi>n</mi>
                        </math>&#160;matrix <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:dsi="http://www.w3.org/1999/xlink">
                           <mfenced separators="">
                              <mi>m</mi>
                              <mo>&#8805;</mo>
                              <mi>n</mi>
                           </mfenced>
                        </math>&#160;                     </td>
                  </tr>
                  <tr>
                     <td class="contents" align="left" valign="top">
                        <a class="rtnref" href="../F01/f01qdc.xml">f01qdc</a>
                        <br/><a class="tocexample" href="../../examples/source/f01qdce.c">Example&#160;Text</a>
                        <br/><a class="tocexample" href="../../examples/data/f01qdce.d">Example&#160;Data</a>
                     </td>
                     <td class="contents" align="left" valign="top">1</td>
                     <td class="contents" align="left" valign="top">
                        <a class="rtnref" href="../F01/f01qdc.xml">nag_real_apply_q</a>
                        <br/>Compute <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:dsi="http://www.w3.org/1999/xlink">
                           <mi>Q</mi>
                           <mi>B</mi>
                        </math>&#160;or <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:dsi="http://www.w3.org/1999/xlink">
                           <msup><mi>Q</mi><mi mathvariant="italic">T</mi></msup>
                           <mi>B</mi>
                        </math>&#160;after <span class="keyword">factorization</span> by <a class="rtnref" href="../F01/f01qcc.xml">nag_real_qr (f01qcc)</a>
                     </td>
                  </tr>
                  <tr>
                     <td class="contents" align="left" valign="top">
                        <a class="rtnref" href="../F01/f01qec.xml">f01qec</a>
                        <br/><a class="tocexample" href="../../examples/source/f01qece.c">Example&#160;Text</a>
                        <br/><a class="tocexample" href="../../examples/data/f01qece.d">Example&#160;Data</a>
                     </td>
                     <td class="contents" align="left" valign="top">1</td>
                     <td class="contents" align="left" valign="top">
                        <a class="rtnref" href="../F01/f01qec.xml">nag_real_form_q</a>
                        <br/>Form <span class="keyword">columns</span> of <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:dsi="http://www.w3.org/1999/xlink">
                           <mi>Q</mi>
                        </math>&#160;after <span class="keyword">factorization</span> by <a class="rtnref" href="../F01/f01qcc.xml">nag_real_qr (f01qcc)</a>
                     </td>
                  </tr>
                  <tr>
                     <td class="contents" align="left" valign="top">
                        <a class="rtnref" href="../F01/f01rcc.xml">f01rcc</a>
                        <br/><a class="tocexample" href="../../examples/source/f01rcce.c">Example&#160;Text</a>
                        <br/><a class="tocexample" href="../../examples/data/f01rcce.d">Example&#160;Data</a>
                     </td>
                     <td class="contents" align="left" valign="top">1</td>
                     <td class="contents" align="left" valign="top">
                        <a class="rtnref" href="../F01/f01rcc.xml">nag_complex_qr</a>
                        <br/>
                        <span class="keyword">
                           <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:dsi="http://www.w3.org/1999/xlink">
                              <mi>Q</mi>
                              <mi>R</mi>
                           </math>&#160;                        </span> 
                        <span class="keyword">factorization</span> of <span class="keyword">complex</span> 
                        <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:dsi="http://www.w3.org/1999/xlink">
                           <mi>m</mi>
                        </math>&#160;by <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:dsi="http://www.w3.org/1999/xlink">
                           <mi>n</mi>
                        </math>&#160;matrix <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:dsi="http://www.w3.org/1999/xlink">
                           <mfenced separators="">
                              <mi>m</mi>
                              <mo>&#8805;</mo>
                              <mi>n</mi>
                           </mfenced>
                        </math>&#160;                     </td>
                  </tr>
                  <tr>
                     <td class="contents" align="left" valign="top">
                        <a class="rtnref" href="../F01/f01rdc.xml">f01rdc</a>
                        <br/><a class="tocexample" href="../../examples/source/f01rdce.c">Example&#160;Text</a>
                        <br/><a class="tocexample" href="../../examples/data/f01rdce.d">Example&#160;Data</a>
                     </td>
                     <td class="contents" align="left" valign="top">1</td>
                     <td class="contents" align="left" valign="top">
                        <a class="rtnref" href="../F01/f01rdc.xml">nag_complex_apply_q</a>
                        <br/>Compute <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:dsi="http://www.w3.org/1999/xlink">
                           <mi>Q</mi>
                           <mi>B</mi>
                        </math>&#160;or <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:dsi="http://www.w3.org/1999/xlink">
                           <msup>
                              <mi>Q</mi>
                              <mi>H</mi>
                           </msup>
                           <mi>B</mi>
                        </math>&#160;after <span class="keyword">factorization</span> by <a class="rtnref" href="../F01/f01rcc.xml">nag_complex_qr (f01rcc)</a>
                     </td>
                  </tr>
                  <tr>
                     <td class="contents" align="left" valign="top">
                        <a class="rtnref" href="../F01/f01rec.xml">f01rec</a>
                        <br/><a class="tocexample" href="../../examples/source/f01rece.c">Example&#160;Text</a>
                        <br/><a class="tocexample" href="../../examples/data/f01rece.d">Example&#160;Data</a>
                     </td>
                     <td class="contents" align="left" valign="top">1</td>
                     <td class="contents" align="left" valign="top">
                        <a class="rtnref" href="../F01/f01rec.xml">nag_complex_form_q</a>
                        <br/>Form <span class="keyword">columns</span> of <math xmlns="http://www.w3.org/1998/Math/MathML" xmlns:dsi="http://www.w3.org/1999/xlink">
                           <mi>Q</mi>
                        </math>&#160;after <span class="keyword">factorization</span> by <a class="rtnref" href="../F01/f01rcc.xml">nag_complex_qr (f01rcc)</a>
                     </td>
                  </tr>
               </tbody>
            </table></div>
      
<hr/><div><a href="f01_intro.xml">Chapter Introduction</a></div><div><a href="../mark7.xml">NAG C Library Contents</a></div>
<div><hr/>
  &#169; The Numerical Algorithms Group Ltd, Oxford, UK. 2004
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