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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="KSPChebyshevEstEigSet"><H1>KSPChebyshevEstEigSet</H1></A>
Automatically estimate the eigenvalues to use for Chebyshev
<H3><FONT COLOR="#CC3333">Synopsis</FONT></H3>
<PRE>
#include "petscksp.h"
PetscErrorCode KSPChebyshevEstEigSet(KSP ksp,PetscReal a,PetscReal b,PetscReal c,PetscReal d)
</PRE>
Logically 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>- the Krylov space context
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>a </B></TD><TD>- multiple of min eigenvalue estimate to use for min Chebyshev bound (or <A HREF="../Sys/PETSC_DECIDE.html#PETSC_DECIDE">PETSC_DECIDE</A>)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>b </B></TD><TD>- multiple of max eigenvalue estimate to use for min Chebyshev bound (or <A HREF="../Sys/PETSC_DECIDE.html#PETSC_DECIDE">PETSC_DECIDE</A>)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>c </B></TD><TD>- multiple of min eigenvalue estimate to use for max Chebyshev bound (or <A HREF="../Sys/PETSC_DECIDE.html#PETSC_DECIDE">PETSC_DECIDE</A>)
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>d </B></TD><TD>- multiple of max eigenvalue estimate to use for max Chebyshev bound (or <A HREF="../Sys/PETSC_DECIDE.html#PETSC_DECIDE">PETSC_DECIDE</A>)
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#CC3333">Options Database</FONT></H3>
<DT><B>-ksp_chebyshev_esteig a,b,c,d</B> -
Notes:
The Chebyshev bounds are set using
<br>
<PRE>
minbound = a*minest + b*maxest
maxbound = c*minest + d*maxest
</PRE>
The default configuration targets the upper part of the spectrum for use as a multigrid smoother, so only the maximum eigenvalue estimate is used.
The minimum eigenvalue estimate obtained by Krylov iteration is typically not accurate until the method has converged.
<P>
If 0.0 is passed for all transform arguments (a,b,c,d), eigenvalue estimation is disabled.
<P>
The default transform is (0,0.1; 0,1.1) which targets the "upper" part of the spectrum, as desirable for use with multigrid.
<P>
The eigenvalues are estimated using the Lanczo (<A HREF="../KSP/KSPCG.html#KSPCG">KSPCG</A>) or Arnoldi (<A HREF="../KSP/KSPGMRES.html#KSPGMRES">KSPGMRES</A>) process using a random right hand side vector.
<P>
<P>
<H3><FONT COLOR="#CC3333">Keywords</FONT></H3>
<A HREF="../KSP/KSP.html#KSP">KSP</A>, Chebyshev, set, eigenvalues, <A HREF="../PC/PCMG.html#PCMG">PCMG</A>
<BR><P><B><P><B><FONT COLOR="#CC3333">Level:</FONT></B>intermediate
<BR><FONT COLOR="#CC3333">Location:</FONT></B><A HREF="../../../src/ksp/ksp/impls/cheby/cheby.c.html#KSPChebyshevEstEigSet">src/ksp/ksp/impls/cheby/cheby.c</A>
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