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<div id="version" align=right><b>slepc-3.23.1 2025-05-01</b></div>
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<H1>PEPCheckDefiniteQEP</H1>
Determines if a symmetric/Hermitian quadratic eigenvalue problem is definite or not.
<H3><FONT COLOR="#883300">Synopsis</FONT></H3>
<PRE>
#include "slepcpep.h"
<A HREF="https://petsc.org/release/manualpages/Sys/PetscErrorCode.html#PetscErrorCode">PetscErrorCode</A> <A HREF="../PEP/PEPCheckDefiniteQEP.html#PEPCheckDefiniteQEP">PEPCheckDefiniteQEP</A>(<A HREF="../PEP/PEP.html#PEP">PEP</A> pep,<A HREF="https://petsc.org/release/manualpages/Sys/PetscReal.html#PetscReal">PetscReal</A> *xi,<A HREF="https://petsc.org/release/manualpages/Sys/PetscReal.html#PetscReal">PetscReal</A> *mu,<A HREF="https://petsc.org/release/manualpages/Sys/PetscInt.html#PetscInt">PetscInt</A> *definite,<A HREF="https://petsc.org/release/manualpages/Sys/PetscInt.html#PetscInt">PetscInt</A> *hyperbolic)
</PRE>
Collective
<P>
<H3><FONT COLOR="#883300">Input Parameter</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>pep </B></TD><TD> - eigensolver context
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#883300">Output Parameters</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>xi </B></TD><TD> - first computed parameter
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>mu </B></TD><TD> - second computed parameter
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>definite </B></TD><TD> - flag indicating that the problem is definite
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>hyperbolic </B></TD><TD> - flag indicating that the problem is hyperbolic
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#883300">Notes</FONT></H3>
This function is intended for quadratic eigenvalue problems, Q(lambda)=A*lambda^2+B*lambda+C,
with symmetric (or Hermitian) coefficient matrices A,B,C.
<P>
On output, the flag 'definite' may have the values -1 (meaning that the QEP is not
definite), 1 (if the problem is definite), or 0 if the algorithm was not able to
determine whether the problem is definite or not.
<P>
If definite=1, the output flag 'hyperbolic' informs in a similar way about whether the
problem is hyperbolic or not.
<P>
If definite=1, the computed values xi and mu satisfy Q(xi)<0 and Q(mu)>0, as
obtained via the method proposed in [Niendorf and Voss, LAA 2010]. Furthermore, if
hyperbolic=1 then only xi is computed.
<P>
<P>
<H3><FONT COLOR="#883300">See Also</FONT></H3>
<A HREF="../PEP/PEPSetProblemType.html#PEPSetProblemType">PEPSetProblemType</A>()
<BR><P><B></B><H3><FONT COLOR="#883300">Level</FONT></H3>advanced<BR>
<H3><FONT COLOR="#883300">Location</FONT></H3>
</B><A HREF="../../../src/pep/impls/krylov/stoar/qslice.c.html#PEPCheckDefiniteQEP">src/pep/impls/krylov/stoar/qslice.c</A>
<P><H3><FONT COLOR="#883300">Examples</FONT></H3>
<A HREF="../../../src/pep/tutorials/ex40.c.html">src/pep/tutorials/ex40.c</A><BR>
<BR><BR><A HREF="./index.html">Index of all PEP routines</A>
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