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<div><a class="htmltoc" href="../FRONTMATTER/manconts.xml">NAG Library Manual</a></div><hr/><h1 class="libdoc">NAG Library Chapter Contents<br/><br/>F04 &#8211; Simultaneous Linear Equations</h1>
<h3 class="standard"><a class="chapint" href="../F04/f04intro.xml">F04 Chapter Introduction</a></h3>
<div class="left-tablediv"><table class="contents"><tbody>
<tr>
<td class="contents" valign="top" align="left"><b>Routine<br/>Name</b></td>
<td class="contents" valign="top" align="center"><b>Mark of<br/>Introduction</b></td>
<td class="contents" valign="top" align="left"><br/><b>Purpose</b></td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04aaf.xml">F04AAF</a>
<br/><a class="tocexample" href="../../examples/source/f04aafe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04aafe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">2</td>
<td class="contentsdoc" valign="top">Solution of real simultaneous linear equations with multiple right-hand sides (Black Box)<br/><b>Note</b>: this routine is scheduled for withdrawal at Mark 23, see <a class="sec" href="../GENINT/replace.xml#F04AAF">Advice on Replacement Calls for Withdrawn/Superseded Routines</a> for further information.</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04abf.xml">F04ABF</a>
<br/><a class="tocexample" href="../../examples/source/f04abfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04abfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">2</td>
<td class="contentsdoc" valign="top">Solution of real symmetric positive-definite simultaneous linear equations with multiple right-hand sides using iterative refinement (Black Box)</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04acf.xml">F04ACF</a>
<br/><a class="tocexample" href="../../examples/source/f04acfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04acfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">2</td>
<td class="contentsdoc" valign="top">Solution of real symmetric positive-definite banded simultaneous linear equations with multiple right-hand sides (Black Box)<br/><b>Note</b>: this routine is scheduled for withdrawal at Mark 23, see <a class="sec" href="../GENINT/replace.xml#F04ACF">Advice on Replacement Calls for Withdrawn/Superseded Routines</a> for further information.</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04adf.xml">F04ADF</a>
<br/><a class="tocexample" href="../../examples/source/f04adfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04adfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">2</td>
<td class="contentsdoc" valign="top">Solution of complex simultaneous linear equations with multiple right-hand sides (Black Box)<br/><b>Note</b>: this routine is scheduled for withdrawal at Mark 23, see <a class="sec" href="../GENINT/replace.xml#F04ADF">Advice on Replacement Calls for Withdrawn/Superseded Routines</a> for further information.</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04aef.xml">F04AEF</a>
<br/><a class="tocexample" href="../../examples/source/f04aefe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04aefe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">2</td>
<td class="contentsdoc" valign="top">Solution of real simultaneous linear equations with multiple right-hand sides using iterative refinement (Black Box)</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04aff.xml">F04AFF</a>
<br/><a class="tocexample" href="../../examples/source/f04affe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04affe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">2</td>
<td class="contentsdoc" valign="top">Solution of real symmetric positive-definite simultaneous linear equations using iterative refinement (coefficient matrix already factorized by <a class="rout" href="../F03/f03aef.xml">F03AEF</a>)</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04agf.xml">F04AGF</a>
<br/><a class="tocexample" href="../../examples/source/f04agfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04agfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">2</td>
<td class="contentsdoc" valign="top">Solution of real symmetric positive-definite simultaneous linear equations (coefficient matrix already factorized by <a class="rout" href="../F03/f03aef.xml">F03AEF</a>)</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04ahf.xml">F04AHF</a>
<br/><a class="tocexample" href="../../examples/source/f04ahfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04ahfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">2</td>
<td class="contentsdoc" valign="top">Solution of real simultaneous linear equations using iterative refinement (coefficient matrix already factorized by <a class="rout" href="../F03/f03aff.xml">F03AFF</a>)</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04ajf.xml">F04AJF</a>
<br/><a class="tocexample" href="../../examples/source/f04ajfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04ajfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">2</td>
<td class="contentsdoc" valign="top">Solution of real simultaneous linear equations (coefficient matrix already factorized by <a class="rout" href="../F03/f03aff.xml">F03AFF</a>)</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04amf.xml">F04AMF</a>
<br/><a class="tocexample" href="../../examples/source/f04amfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04amfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">2</td>
<td class="contentsdoc" valign="top">Least-squares solution of <m:math><m:mi>m</m:mi></m:math>real equations in <m:math><m:mi>n</m:mi></m:math>&#160;unknowns, rank <m:math><m:mtext/><m:mo>=</m:mo><m:mi>n</m:mi></m:math>, <m:math><m:mi>m</m:mi><m:mo>&#8805;</m:mo><m:mi>n</m:mi></m:math>&#160;using iterative refinement (Black Box)</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04arf.xml">F04ARF</a>
<br/><a class="tocexample" href="../../examples/source/f04arfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04arfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">4</td>
<td class="contentsdoc" valign="top">Solution of real simultaneous linear equations, one right-hand side (Black Box)<br/><b>Note</b>: this routine is scheduled for withdrawal at Mark 23, see <a class="sec" href="../GENINT/replace.xml#F04ARF">Advice on Replacement Calls for Withdrawn/Superseded Routines</a> for further information.</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04asf.xml">F04ASF</a>
<br/><a class="tocexample" href="../../examples/source/f04asfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04asfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">4</td>
<td class="contentsdoc" valign="top">Solution of real symmetric positive-definite simultaneous linear equations, one right-hand side using iterative refinement (Black Box)</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04atf.xml">F04ATF</a>
<br/><a class="tocexample" href="../../examples/source/f04atfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04atfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">4</td>
<td class="contentsdoc" valign="top">Solution of real simultaneous linear equations, one right-hand side using iterative refinement (Black Box)</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04axf.xml">F04AXF</a>
<br/><a class="tocexample" href="../../examples/source/f04axfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04axfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">7</td>
<td class="contentsdoc" valign="top">Solution of real sparse simultaneous linear equations (coefficient matrix already factorized)</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04baf.xml">F04BAF</a>
<br/><a class="tocexample" href="../../examples/source/f04bafe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04bafe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">21</td>
<td class="contentsdoc" valign="top">Computes the solution and error-bound to a real system of linear equations</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04bbf.xml">F04BBF</a>
<br/><a class="tocexample" href="../../examples/source/f04bbfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04bbfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">21</td>
<td class="contentsdoc" valign="top">Computes the solution and error-bound to a real banded system of linear equations</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04bcf.xml">F04BCF</a>
<br/><a class="tocexample" href="../../examples/source/f04bcfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04bcfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">21</td>
<td class="contentsdoc" valign="top">Computes the solution and error-bound to a real tridiagonal system of linear equations</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04bdf.xml">F04BDF</a>
<br/><a class="tocexample" href="../../examples/source/f04bdfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04bdfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">21</td>
<td class="contentsdoc" valign="top">Computes the solution and error-bound to a real symmetric positive-definite system of linear equations</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04bef.xml">F04BEF</a>
<br/><a class="tocexample" href="../../examples/source/f04befe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04befe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">21</td>
<td class="contentsdoc" valign="top">Computes the solution and error-bound to a real symmetric positive-definite system of linear equations, packed storage</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04bff.xml">F04BFF</a>
<br/><a class="tocexample" href="../../examples/source/f04bffe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04bffe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">21</td>
<td class="contentsdoc" valign="top">Computes the solution and error-bound to a real symmetric positive-definite banded system of linear equations</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04bgf.xml">F04BGF</a>
<br/><a class="tocexample" href="../../examples/source/f04bgfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04bgfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">21</td>
<td class="contentsdoc" valign="top">Computes the solution and error-bound to a real symmetric positive-definite tridiagonal system of linear equations</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04bhf.xml">F04BHF</a>
<br/><a class="tocexample" href="../../examples/source/f04bhfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04bhfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">21</td>
<td class="contentsdoc" valign="top">Computes the solution and error-bound to a real symmetric system of linear equations</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04bjf.xml">F04BJF</a>
<br/><a class="tocexample" href="../../examples/source/f04bjfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04bjfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">21</td>
<td class="contentsdoc" valign="top">Computes the solution and error-bound to a real symmetric system of linear equations, packed storage</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04caf.xml">F04CAF</a>
<br/><a class="tocexample" href="../../examples/source/f04cafe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04cafe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">21</td>
<td class="contentsdoc" valign="top">Computes the solution and error-bound to a complex system of linear equations</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04cbf.xml">F04CBF</a>
<br/><a class="tocexample" href="../../examples/source/f04cbfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04cbfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">21</td>
<td class="contentsdoc" valign="top">Computes the solution and error-bound to a complex banded system of linear equations</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04ccf.xml">F04CCF</a>
<br/><a class="tocexample" href="../../examples/source/f04ccfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04ccfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">21</td>
<td class="contentsdoc" valign="top">Computes the solution and error-bound to a complex tridiagonal system of linear equations</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04cdf.xml">F04CDF</a>
<br/><a class="tocexample" href="../../examples/source/f04cdfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04cdfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">21</td>
<td class="contentsdoc" valign="top">Computes the solution and error-bound to a complex Hermitian positive-definite system of linear equations</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04cef.xml">F04CEF</a>
<br/><a class="tocexample" href="../../examples/source/f04cefe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04cefe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">21</td>
<td class="contentsdoc" valign="top">Computes the solution and error-bound to a complex Hermitian positive-definite system of linear equations, packed storage</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04cff.xml">F04CFF</a>
<br/><a class="tocexample" href="../../examples/source/f04cffe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04cffe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">21</td>
<td class="contentsdoc" valign="top">Computes the solution and error-bound to a complex Hermitian positive-definite banded system of linear equations</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04cgf.xml">F04CGF</a>
<br/><a class="tocexample" href="../../examples/source/f04cgfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04cgfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">21</td>
<td class="contentsdoc" valign="top">Computes the solution and error-bound to a complex Hermitian positive-definite tridiagonal system of linear equations</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04chf.xml">F04CHF</a>
<br/><a class="tocexample" href="../../examples/source/f04chfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04chfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">21</td>
<td class="contentsdoc" valign="top">Computes the solution and error-bound to a complex Hermitian system of linear equations</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04cjf.xml">F04CJF</a>
<br/><a class="tocexample" href="../../examples/source/f04cjfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04cjfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">21</td>
<td class="contentsdoc" valign="top">Computes the solution and error-bound to a complex Hermitian system of linear equations, packed storage</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04dhf.xml">F04DHF</a>
<br/><a class="tocexample" href="../../examples/source/f04dhfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04dhfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">21</td>
<td class="contentsdoc" valign="top">Computes the solution and error-bound to a complex symmetric system of linear equations</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04djf.xml">F04DJF</a>
<br/><a class="tocexample" href="../../examples/source/f04djfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04djfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">21</td>
<td class="contentsdoc" valign="top">Computes the solution and error-bound to a complex symmetric system of linear equations, packed storage.</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04eaf.xml">F04EAF</a>
<br/><a class="tocexample" href="../../examples/source/f04eafe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04eafe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">11</td>
<td class="contentsdoc" valign="top">Solution of real tridiagonal simultaneous linear equations, one right-hand side (Black Box)<br/><b>Note</b>: this routine is scheduled for withdrawal at Mark 23, see <a class="sec" href="../GENINT/replace.xml#F04EAF">Advice on Replacement Calls for Withdrawn/Superseded Routines</a> for further information.</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04faf.xml">F04FAF</a>
<br/><a class="tocexample" href="../../examples/source/f04fafe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04fafe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">11</td>
<td class="contentsdoc" valign="top">Solution of real symmetric positive-definite tridiagonal simultaneous linear equations, one right-hand side (Black Box)<br/><b>Note</b>: this routine is scheduled for withdrawal at Mark 23, see <a class="sec" href="../GENINT/replace.xml#F04FAF">Advice on Replacement Calls for Withdrawn/Superseded Routines</a> for further information.</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04fef.xml">F04FEF</a>
<br/><a class="tocexample" href="../../examples/source/f04fefe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04fefe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">15</td>
<td class="contentsdoc" valign="top">Solution of the Yule&#8211;Walker equations for real symmetric positive-definite Toeplitz matrix, one right-hand side</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04fff.xml">F04FFF</a>
<br/><a class="tocexample" href="../../examples/source/f04fffe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04fffe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">15</td>
<td class="contentsdoc" valign="top">Solution of real symmetric positive-definite Toeplitz system, one right-hand side</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04jaf.xml">F04JAF</a>
<br/><a class="tocexample" href="../../examples/source/f04jafe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04jafe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">Minimal least-squares solution of <m:math><m:mi>m</m:mi></m:math>real equations in <m:math><m:mi>n</m:mi></m:math>&#160;unknowns, rank <m:math><m:mtext/><m:mo>&#8804;</m:mo><m:mi>n</m:mi></m:math>, <m:math><m:mi>m</m:mi><m:mo>&#8805;</m:mo><m:mi>n</m:mi></m:math><br/><b>Note</b>: this routine is scheduled for withdrawal at Mark 23, see <a class="sec" href="../GENINT/replace.xml#F04JAF">Advice on Replacement Calls for Withdrawn/Superseded Routines</a> for further information.</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04jdf.xml">F04JDF</a>
<br/><a class="tocexample" href="../../examples/source/f04jdfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04jdfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">Minimal least-squares solution of <m:math><m:mi>m</m:mi></m:math>real equations in <m:math><m:mi>n</m:mi></m:math>&#160;unknowns, rank <m:math><m:mtext/><m:mo>&#8804;</m:mo><m:mi>m</m:mi></m:math>, <m:math><m:mi>m</m:mi><m:mo>&#8804;</m:mo><m:mi>n</m:mi></m:math><br/><b>Note</b>: this routine is scheduled for withdrawal at Mark 23, see <a class="sec" href="../GENINT/replace.xml#F04JDF">Advice on Replacement Calls for Withdrawn/Superseded Routines</a> for further information.</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04jgf.xml">F04JGF</a>
<br/><a class="tocexample" href="../../examples/source/f04jgfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04jgfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">Least-squares (if rank <m:math><m:mtext/><m:mo>=</m:mo><m:mi>n</m:mi></m:math>) or minimal least-squares (if rank <m:math><m:mtext/><m:mo>&lt;</m:mo><m:mi>n</m:mi></m:math>) solution of <m:math><m:mi>m</m:mi></m:math>real equations in <m:math><m:mi>n</m:mi></m:math>&#160;unknowns, <m:math><m:mi>m</m:mi><m:mo>&#8805;</m:mo><m:mi>n</m:mi></m:math></td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04jlf.xml">F04JLF</a>
<br/><a class="tocexample" href="../../examples/source/f04jlfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04jlfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">17</td>
<td class="contentsdoc" valign="top">Real general Gauss&#8211;Markov linear model (including weighted least-squares)<br/><b>Note</b>: this routine is scheduled for withdrawal at Mark 23, see <a class="sec" href="../GENINT/replace.xml#F04JLF">Advice on Replacement Calls for Withdrawn/Superseded Routines</a> for further information.</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04jmf.xml">F04JMF</a>
<br/><a class="tocexample" href="../../examples/source/f04jmfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04jmfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">17</td>
<td class="contentsdoc" valign="top">Equality-constrained real linear least-squares problem<br/><b>Note</b>: this routine is scheduled for withdrawal at Mark 23, see <a class="sec" href="../GENINT/replace.xml#F04JMF">Advice on Replacement Calls for Withdrawn/Superseded Routines</a> for further information.</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04klf.xml">F04KLF</a>
<br/><a class="tocexample" href="../../examples/source/f04klfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04klfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">17</td>
<td class="contentsdoc" valign="top">Complex general Gauss&#8211;Markov linear model (including weighted least-squares)<br/><b>Note</b>: this routine is scheduled for withdrawal at Mark 23, see <a class="sec" href="../GENINT/replace.xml#F04KLF">Advice on Replacement Calls for Withdrawn/Superseded Routines</a> for further information.</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04kmf.xml">F04KMF</a>
<br/><a class="tocexample" href="../../examples/source/f04kmfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04kmfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">17</td>
<td class="contentsdoc" valign="top">Equality-constrained complex linear least-squares problem<br/><b>Note</b>: this routine is scheduled for withdrawal at Mark 23, see <a class="sec" href="../GENINT/replace.xml#F04KMF">Advice on Replacement Calls for Withdrawn/Superseded Routines</a> for further information.</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04lef.xml">F04LEF</a>
<br/><a class="tocexample" href="../../examples/source/f04lefe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04lefe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">11</td>
<td class="contentsdoc" valign="top">Solution of real tridiagonal simultaneous linear equations (coefficient matrix already factorized by <a class="rout" href="../F01/f01lef.xml">F01LEF</a>)</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04lhf.xml">F04LHF</a>
<br/><a class="tocexample" href="../../examples/source/f04lhfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04lhfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">13</td>
<td class="contentsdoc" valign="top">Solution of real almost block diagonal simultaneous linear equations (coefficient matrix already factorized by <a class="rout" href="../F01/f01lhf.xml">F01LHF</a>)</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04mcf.xml">F04MCF</a>
<br/><a class="tocexample" href="../../examples/source/f04mcfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04mcfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">8</td>
<td class="contentsdoc" valign="top">Solution of real symmetric positive-definite variable-bandwidth simultaneous linear equations (coefficient matrix already factorized by <a class="rout" href="../F01/f01mcf.xml">F01MCF</a>)</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04mef.xml">F04MEF</a>
<br/><a class="tocexample" href="../../examples/source/f04mefe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04mefe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">15</td>
<td class="contentsdoc" valign="top">Update solution of the Yule&#8211;Walker equations for real symmetric positive-definite Toeplitz matrix</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04mff.xml">F04MFF</a>
<br/><a class="tocexample" href="../../examples/source/f04mffe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04mffe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">15</td>
<td class="contentsdoc" valign="top">Update solution of real symmetric positive-definite Toeplitz system</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04qaf.xml">F04QAF</a>
<br/><a class="tocexample" href="../../examples/source/f04qafe.f">Example&#160;Text</a></td>
<td class="contentsdoc" valign="top" align="center">11</td>
<td class="contentsdoc" valign="top">Sparse linear least-squares problem, <m:math><m:mi>m</m:mi></m:math>real equations in <m:math><m:mi>n</m:mi></m:math>&#160;unknowns</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04yaf.xml">F04YAF</a>
<br/><a class="tocexample" href="../../examples/source/f04yafe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04yafe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">11</td>
<td class="contentsdoc" valign="top">Covariance matrix for linear least-squares problems, <m:math><m:mi>m</m:mi></m:math>real equations in <m:math><m:mi>n</m:mi></m:math>&#160;unknowns</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04ycf.xml">F04YCF</a>
<br/><a class="tocexample" href="../../examples/source/f04ycfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04ycfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">13</td>
<td class="contentsdoc" valign="top">Norm estimation (for use in condition estimation), real matrix</td>
</tr>
<tr>
<td class="contentsdoc" valign="top"><a class="rout" href="../F04/f04zcf.xml">F04ZCF</a>
<br/><a class="tocexample" href="../../examples/source/f04zcfe.f">Example&#160;Text</a><br/>
<a class="tocexample" href="../../examples/data/f04zcfe.d">Example&#160;Data</a></td>
<td class="contentsdoc" valign="top" align="center">13</td>
<td class="contentsdoc" valign="top">Norm estimation (for use in condition estimation), complex matrix</td>
</tr>
</tbody>
</table></div><hr/><div><a class="chap" href="../../pdf/F04/f04conts.pdf">F04 Chapter Contents (PDF version)</a></div><div><a class="chapint" href="f04intro.xml">F04 Chapter Introduction</a></div>
<div><a class="htmltoc" href="../FRONTMATTER/manconts.xml">NAG Library Manual</a></div>
<div><hr/><a class="genint" href="../FRONTMATTER/copyright.xml">&#169; The Numerical Algorithms Group Ltd, Oxford, UK. 2009</a></div></body></html>
