📄 qmrconstmatrixvectorconstvectorbconstprecond1constprecond2iteration.html
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It is provided "as is" without express or implied warranty. -- --><HEAD><TITLE>Description of qmr</TITLE></HEAD><BODY BGCOLOR="#ffffff" LINK="#0000ee" TEXT="#000000" VLINK="#551a8b" ALINK="#ff0000"> <FONT FACE=Helvetica><!--end header--><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=2 WIDTH=100%><TR><TD><TABLE BORDER=0 CELLSPACING=0 CELLPADDING=0 WIDTH=100%><TR><TD Align=left valign=middle width=440 rowspan=2><FONT FACE=verdana,arial,helvetica SIZE=+3 COLOR=#110088><B>qmr</B></FONT></TD><TD valign=middle Align=right width=128 rowspan=2><A HREF="http://lsc.nd.edu/research/mtl"><IMG BORDER=0 SRC="./glossy-mtl-logo.jpg" height=48 ALT="[MTL Home]"></A></TD><TD Align=center width=280 nowrap><Font face=verdana,arial,helvetica size=+3><b>Programmers Guide</b></font></TD></TR><TR BGCOLOR='#2020b0'><TD HEIGHT=20 VALIGN='MIDDLE' NOWRAP align=center STYLE="font-family:verdana,arial,helvetica;font-weight:bold;"> <A STYLE="text-decoration:none;color:white;font-family:verdana,arial,helvetica;font-weight:bold;" HREF="./table_of_contents.html">Contents</A> | <A STYLE="text-decoration:none;color:white;font-family:verdana,arial,helvetica;font-weight:bold;" HREF="./mtl_index.html">Index</A> | <A STYLE="text-decoration:none;color:white;font-family:verdana,arial,helvetica;font-weight:bold;" HREF="http://lsc.nd.edu/research/mtl/search.html">Search</A> </TD></TR></TABLE></TD></TR><TR><TD><Table CellPadding=0 CellSpacing=0 width=100% cols=2><TR><TD Align=left><BR><TABLE BORDER=0 CellSpacing=0 CellPadding=0><TR><TD><Img src = "itl.gif" Alt="" WIDTH = "194" HEIGHT = "38" ></TD></TR><TR><TD><Img src = "algorithms.gif" Alt="" WIDTH = "194" HEIGHT = "38" ></TD></TR></TABLE></TD><TD Align=right><BR><TABLE BORDER=0 CellSpacing=0 CellPadding=0><TR><TD><Img src = "function.gif" Alt="" WIDTH = "194" HEIGHT = "38" ></TD></TR></TABLE></TD></TR><TR><TD Align=left VAlign=top><b>Category</b>:itl,algorithms</TD><TD Align=right VAlign=top><b>Component type</b>:function</TD></TR></Table></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="10" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>Prototype</B></FONT></TD></TR><TR><TD><TT>template <class <A HREF="Matrix.html" >Matrix</A>, class <A HREF="Vector.html" >Vector</A>, class VectorB, class Precond1, class Precond2, class <A HREF="Iteration.html" >Iteration</A>><br> int <B>qmr</B>(const <A HREF="Matrix.html" >Matrix</A> &A, <A HREF="Vector.html" >Vector</A> &x, const VectorB &b, const Precond1 &M1, const Precond2 &M2, <A HREF="Iteration.html" >Iteration</A>& iter) ;</TT></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="10" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>Description</B></FONT></TD></TR><TR><TD> This routine solves the unsymmetric linear system Ax = b using the Quasi-Minimal Residual method.<table align=center border=1> <tr><td> return value </td> <td> meaning </td> </tr> <tr><td> 0 </td><td> convergence within maximum iterations </td> </tr> <tr><td> 1 </td><td> no convergence after maximum iterations</td> </tr> <tr><td> 2 </td><td> breakdown in rho </td> </tr> <tr><td> 3 </td><td> breakdown in beta </td> </tr> <tr><td> 4 </td><td> breakdown in gamma</td> </tr> <tr><td> 5 </td><td> breakdown in delta</td> </tr> <tr><td> 6 </td><td> breakdown in ep</td> </tr> <tr><td> 7 </td><td> breakdown in xi</td> </tr> </table>See: R. W. Freund and N. M. Nachtigal, A quasi-minimal residual method for non-Hermitian linear systems, Numerical Math., 60(1991), pp. 315-339</TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="10" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>Definition</B></FONT></TD></TR><TR><TD><A HREF="../../../contrib/itl/itl/qmr.h">qmr.h</A></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="10" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>Preconditions</B></FONT></TD></TR><TR><TD><UL></UL></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="10" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>Complexity</B></FONT></TD></TR><TR><TD></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="10" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>Example</B></FONT></TD></TR><TR><TD>In <A HREF=../../contrib/examples/qmr.cc>qmr.cc</A>:<PRE> <A HREF="Matrix.html" >Matrix</A> A(5, 5); // Fill <A HREF="matrix.html" >matrix</A>... dense1D<Type> x(A.nrows(), Type(0)); dense1D<Type> b(A.ncols()); for (dense1D<Type>::iterator i=b.begin(); i!=b.end(); i++) *i = 1.; //<A HREF="SSOR.html" >SSOR</A> preconditioner <A HREF="SSOR.html" >SSOR</A><<A HREF="Matrix.html" >Matrix</A>> precond(A); //iteration noisy_iteration<double> iter(b, max_iter, 1e-6); //qmr algorithm qmr(A, x, b, precond.left(), precond.right(), iter);</PRE></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="10" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>Notes</B></FONT></TD></TR><TR><TD></TD></TR><TR><TD><IMG SRC="whitespace.gif" Alt="" WIDTH="32" HEIGHT="15" ALIGN="TOP"></TD></TR><TR BGCOLOR=#e0e0e0><TD VALIGN=BOTTOM><FONT FACE=arial,helvetica SIZE=+1><B>See also</B></FONT></TD></TR><TR><TD></TD></TR></TABLE><!--start footer--> <P><CENTER><CENTER><IMG SRC="./blue-bar.jpg" width=640></CENTER></CENTER><P><A HREF="http://www.nd.edu"><IMG BORDER=0 SRC="./ndtoclogo.gif" ALT="[MTL Home]" ALIGN=absmiddle></A></A><FONT SIZE="-2"><A HREF="../LICENSE.htm">Copyright ©1998,1999 University of Notre Dame. 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