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<div id="version" align=right><b>petsc-3.7.5 2017-01-01</b></div>
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<A NAME="KSPCHEBYSHEV"><H1>KSPCHEBYSHEV</H1></A>
The preconditioned Chebyshev iterative method
<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_chebyshev_eigenvalues <emin,emax> </B></TD><TD>- set approximations to the smallest and largest eigenvalues
of the preconditioned operator. If these are accurate you will get much faster convergence.
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_chebyshev_esteig <a,b,c,d> </B></TD><TD>- estimate eigenvalues using a Krylov method, then use this
transform for Chebyshev eigenvalue bounds (<A HREF="../KSP/KSPChebyshevEstEigSet.html#KSPChebyshevEstEigSet">KSPChebyshevEstEigSet</A>())
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_chebyshev_esteig_steps </B></TD><TD>- number of estimation steps
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-ksp_chebyshev_esteig_random </B></TD><TD>- use random number generator to create right hand side for eigenvalue estimator
</TD></TR></TABLE>
<P>
<P>
Notes: The Chebyshev method requires both the matrix and preconditioner to
be symmetric positive (semi) definite.
Only support for left preconditioning.
<P>
Chebyshev is configured as a smoother by default, targetting the "upper" part of the spectrum.
The user should call <A HREF="../KSP/KSPChebyshevSetEigenvalues.html#KSPChebyshevSetEigenvalues">KSPChebyshevSetEigenvalues</A>() if they have eigenvalue estimates.
<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>,
<BR><A HREF="../KSP/KSPChebyshevSetEigenvalues.html#KSPChebyshevSetEigenvalues">KSPChebyshevSetEigenvalues</A>(), <A HREF="../KSP/KSPChebyshevEstEigSet.html#KSPChebyshevEstEigSet">KSPChebyshevEstEigSet</A>(), <A HREF="../KSP/KSPChebyshevEstEigSetUseRandom.html#KSPChebyshevEstEigSetUseRandom">KSPChebyshevEstEigSetUseRandom</A>(), <A HREF="../KSP/KSPChebyshevEstEigSetRandom.html#KSPChebyshevEstEigSetRandom">KSPChebyshevEstEigSetRandom</A>(),
<A HREF="../KSP/KSPRICHARDSON.html#KSPRICHARDSON">KSPRICHARDSON</A>, <A HREF="../KSP/KSPCG.html#KSPCG">KSPCG</A>, <A HREF="../PC/PCMG.html#PCMG">PCMG</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/cheby/cheby.c.html#KSPCHEBYSHEV">src/ksp/ksp/impls/cheby/cheby.c</A>
<BR><A HREF="./index.html">Index of all KSP routines</A>
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