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<div id="version" align=right><b>petsc-3.4.2 2013-07-02</b></div>
<A NAME="KSPGMRES"><H1>KSPGMRES</H1></A>
Implements the Generalized Minimal Residual method. (Saad and Schultz, 1986) with restart
<P>
<H3><FONT COLOR="#CC3333">Options Database Keys</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_gmres_restart <restart> </B></TD><TD>- the number of Krylov directions to orthogonalize against
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_gmres_haptol <tol> </B></TD><TD>- sets the tolerance for "happy ending" (exact convergence)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_gmres_preallocate </B></TD><TD>- preallocate all the Krylov search directions initially (otherwise groups of
vectors are allocated as needed)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_gmres_classicalgramschmidt </B></TD><TD>- use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_gmres_modifiedgramschmidt </B></TD><TD>- use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_gmres_cgs_refinement_type <never,ifneeded,always> </B></TD><TD>- determine if iterative refinement is used to increase the
stability of the classical Gram-Schmidt orthogonalization.
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_gmres_krylov_monitor </B></TD><TD>- plot the Krylov space generated
</TD></TR></TABLE>
<P>
<P>
Notes: Left and right preconditioning are supported, but not symmetric preconditioning.
<P>
<H3><FONT COLOR="#CC3333">References</FONT></H3>
GMRES: A GENERALIZED MINIMAL RESIDUAL ALGORITHM FOR SOLVING NONSYMMETRIC LINEAR SYSTEMS. YOUCEF SAAD AND MARTIN H. SCHULTZ,
SIAM J. ScI. STAT. COMPUT. Vo|. 7, No. 3, July 1986, pp. 856--869.
<P>
<H3><FONT COLOR="#CC3333">See Also</FONT></H3>
<A HREF="../KSP/KSPCreate.html#KSPCreate">KSPCreate</A>(), <A HREF="../KSP/KSPSetType.html#KSPSetType">KSPSetType</A>(), <A HREF="../KSP/KSPType.html#KSPType">KSPType</A> (for list of available types), <A HREF="../KSP/KSP.html#KSP">KSP</A>, <A HREF="../KSP/KSPFGMRES.html#KSPFGMRES">KSPFGMRES</A>, <A HREF="../KSP/KSPLGMRES.html#KSPLGMRES">KSPLGMRES</A>,
<BR><A HREF="../KSP/KSPGMRESSetRestart.html#KSPGMRESSetRestart">KSPGMRESSetRestart</A>(), <A HREF="../KSP/KSPGMRESSetHapTol.html#KSPGMRESSetHapTol">KSPGMRESSetHapTol</A>(), <A HREF="../KSP/KSPGMRESSetPreAllocateVectors.html#KSPGMRESSetPreAllocateVectors">KSPGMRESSetPreAllocateVectors</A>(), <A HREF="../KSP/KSPGMRESSetOrthogonalization.html#KSPGMRESSetOrthogonalization">KSPGMRESSetOrthogonalization</A>(), <A HREF="../KSP/KSPGMRESGetOrthogonalization.html#KSPGMRESGetOrthogonalization">KSPGMRESGetOrthogonalization</A>(),
<A HREF="../KSP/KSPGMRESClassicalGramSchmidtOrthogonalization.html#KSPGMRESClassicalGramSchmidtOrthogonalization">KSPGMRESClassicalGramSchmidtOrthogonalization</A>(), <A HREF="../KSP/KSPGMRESModifiedGramSchmidtOrthogonalization.html#KSPGMRESModifiedGramSchmidtOrthogonalization">KSPGMRESModifiedGramSchmidtOrthogonalization</A>(),
<A HREF="../KSP/KSPGMRESCGSRefinementType.html#KSPGMRESCGSRefinementType">KSPGMRESCGSRefinementType</A>, <A HREF="../KSP/KSPGMRESSetCGSRefinementType.html#KSPGMRESSetCGSRefinementType">KSPGMRESSetCGSRefinementType</A>(), <A HREF="../KSP/KSPGMRESGetCGSRefinementType.html#KSPGMRESGetCGSRefinementType">KSPGMRESGetCGSRefinementType</A>(), <A HREF="../KSP/KSPGMRESMonitorKrylov.html#KSPGMRESMonitorKrylov">KSPGMRESMonitorKrylov</A>(), <A HREF="../KSP/KSPSetPCSide.html#KSPSetPCSide">KSPSetPCSide</A>()
<P>
<P><B><P><B><FONT COLOR="#CC3333">Level:</FONT></B>beginner
<BR><FONT COLOR="#CC3333">Location:</FONT></B><A HREF="../../../src/ksp/ksp/impls/gmres/gmres.c.html#KSPGMRES">src/ksp/ksp/impls/gmres/gmres.c</A>
<BR><A HREF="./index.html">Index of all KSP routines</A>
<BR><A HREF="../../index.html">Table of Contents for all manual pages</A>
<BR><A HREF="../singleindex.html">Index of all manual pages</A>
<P><H3><FONT COLOR="#CC3333">Examples</FONT></H3>
<A HREF="../../../src/ksp/ksp/examples/tutorials/ex7.c.html">src/ksp/ksp/examples/tutorials/ex7.c.html</A><BR>
<A HREF="../../../src/ksp/ksp/examples/tutorials/ex8.c.html">src/ksp/ksp/examples/tutorials/ex8.c.html</A><BR>
<A HREF="../../../src/ksp/ksp/examples/tutorials/ex8g.c.html">src/ksp/ksp/examples/tutorials/ex8g.c.html</A><BR>
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