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<div id="version" align=right><b>petsc-3.10.3 2018-12-18</b></div>
<div id="bugreport" align=right><a href="mailto:petsc-maint@mcs.anl.gov?subject=Typo or Error in Documentation &body=Please describe the typo or error in the documentation: petsc-3.10.3 v3.10.3 docs/manualpages/KSP/KSPLSQRConvergedDefault.html "><small>Report Typos and Errors</small></a></div>
<A NAME="KSPLSQRConvergedDefault"><H1>KSPLSQRConvergedDefault</H1></A>
Determines convergence of the LSQR Krylov method.
<H3><FONT COLOR="#CC3333">Synopsis</FONT></H3>
<PRE>
#include "petscksp.h"
<A HREF="../Sys/PetscErrorCode.html#PetscErrorCode">PetscErrorCode</A> <A HREF="../KSP/KSPLSQRConvergedDefault.html#KSPLSQRConvergedDefault">KSPLSQRConvergedDefault</A>(<A HREF="../KSP/KSP.html#KSP">KSP</A> ksp,<A HREF="../Sys/PetscInt.html#PetscInt">PetscInt</A> n,<A HREF="../Sys/PetscReal.html#PetscReal">PetscReal</A> rnorm,<A HREF="../KSP/KSPConvergedReason.html#KSPConvergedReason">KSPConvergedReason</A> *reason,void *ctx)
</PRE>
Collective on <A HREF="../KSP/KSP.html#KSP">KSP</A>
<P>
<H3><FONT COLOR="#CC3333">Input Parameters</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>ksp </B></TD><TD>- iterative context
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>n </B></TD><TD>- iteration number
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>rnorm </B></TD><TD>- 2-norm residual value (may be estimated)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>ctx </B></TD><TD>- convergence context which must be created by <A HREF="../KSP/KSPConvergedDefaultCreate.html#KSPConvergedDefaultCreate">KSPConvergedDefaultCreate</A>()
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#CC3333">reason is set to</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>positive </B></TD><TD>- if the iteration has converged;
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>negative </B></TD><TD>- if residual norm exceeds divergence threshold;
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>0 </B></TD><TD>- otherwise.
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#CC3333">Notes</FONT></H3>
<A HREF="../KSP/KSPConvergedDefault.html#KSPConvergedDefault">KSPConvergedDefault</A>() is called first to check for convergence in A*x=b.
If that does not determine convergence then checks convergence for the least squares problem, i.e. in min{|b-A*x|}.
Possible convergence for the least squares problem (which is based on the residual of the normal equations) are <A HREF="../KSP/KSPConvergedReason.html#KSPConvergedReason">KSP_CONVERGED_RTOL_NORMAL</A> norm and <A HREF="../KSP/KSPConvergedReason.html#KSPConvergedReason">KSP_CONVERGED_ATOL_NORMAL</A>.
<A HREF="../KSP/KSPConvergedReason.html#KSPConvergedReason">KSP_CONVERGED_RTOL_NORMAL</A> is returned if ||A'*r|| < rtol * ||A|| * ||r||.
Matrix norm ||A|| is iteratively refined estimate, see <A HREF="../KSP/KSPLSQRGetNorms.html#KSPLSQRGetNorms">KSPLSQRGetNorms</A>().
This criterion is now largely compatible with that in MATLAB lsqr().
<P>
<P>
<H3><FONT COLOR="#CC3333">Keywords</FONT></H3>
<A HREF="../KSP/KSP.html#KSP">KSP</A>, <A HREF="../KSP/KSPLSQR.html#KSPLSQR">KSPLSQR</A>, default, convergence, residual
<BR>
<P>
<H3><FONT COLOR="#CC3333">See Also</FONT></H3>
<A HREF="../KSP/KSPLSQR.html#KSPLSQR">KSPLSQR</A>, <A HREF="../KSP/KSPSetConvergenceTest.html#KSPSetConvergenceTest">KSPSetConvergenceTest</A>(), <A HREF="../KSP/KSPSetTolerances.html#KSPSetTolerances">KSPSetTolerances</A>(), <A HREF="../KSP/KSPConvergedSkip.html#KSPConvergedSkip">KSPConvergedSkip</A>(), <A HREF="../KSP/KSPConvergedReason.html#KSPConvergedReason">KSPConvergedReason</A>, <A HREF="../KSP/KSPGetConvergedReason.html#KSPGetConvergedReason">KSPGetConvergedReason</A>(),
<BR><A HREF="../KSP/KSPConvergedDefaultSetUIRNorm.html#KSPConvergedDefaultSetUIRNorm">KSPConvergedDefaultSetUIRNorm</A>(), <A HREF="../KSP/KSPConvergedDefaultSetUMIRNorm.html#KSPConvergedDefaultSetUMIRNorm">KSPConvergedDefaultSetUMIRNorm</A>(), <A HREF="../KSP/KSPConvergedDefaultCreate.html#KSPConvergedDefaultCreate">KSPConvergedDefaultCreate</A>(), <A HREF="../KSP/KSPConvergedDefaultDestroy.html#KSPConvergedDefaultDestroy">KSPConvergedDefaultDestroy</A>(), <A HREF="../KSP/KSPConvergedDefault.html#KSPConvergedDefault">KSPConvergedDefault</A>(), <A HREF="../KSP/KSPLSQRGetNorms.html#KSPLSQRGetNorms">KSPLSQRGetNorms</A>(), <A HREF="../KSP/KSPLSQRSetExactMatNorm.html#KSPLSQRSetExactMatNorm">KSPLSQRSetExactMatNorm</A>()
<P><B></B><H3><FONT COLOR="#CC3333">Level</FONT></H3>intermediate<BR>
<H3><FONT COLOR="#CC3333">Location</FONT></H3>
</B><A HREF="../../../src/ksp/ksp/impls/lsqr/lsqr.c.html#KSPLSQRConvergedDefault">src/ksp/ksp/impls/lsqr/lsqr.c</A>
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