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<div id="version" align=right><b>slepc-3.23.1 2025-05-01</b></div>
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<H1>DSNHEPTS</H1>
Dense Non-Hermitian Eigenvalue Problem (special variant intended for two-sided Krylov solvers).
<P>
<H3><FONT COLOR="#883300">Notes</FONT></H3>
Two related problems are solved, A*X = X*Lambda and B*Y = Y*Lambda', where A and
B are supposed to come from the Arnoldi factorizations of a certain matrix and its
(conjugate) transpose, respectively. Hence, in exact arithmetic the columns of Y
are equal to the left eigenvectors of A. Lambda is a diagonal matrix whose diagonal
elements are the arguments of <A HREF="../DS/DSSolve.html#DSSolve">DSSolve</A>(). After solve, A is overwritten with the
upper quasi-triangular matrix T of the (real) Schur form, A*Q = Q*T, and similarly
another (real) Schur relation is computed, B*Z = Z*S, overwriting B.
<P>
In the intermediate state A and B are reduced to upper Hessenberg form.
<P>
When left eigenvectors <A HREF="../DS/DSMatType.html#DSMatType">DS_MAT_Y</A> are requested, right eigenvectors of B are returned,
while <A HREF="../DS/DSMatType.html#DSMatType">DS_MAT_X</A> contains right eigenvectors of A.
<P>
<H3><FONT COLOR="#883300">Used DS matrices</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B><A HREF="../DS/DSMatType.html#DSMatType">DS_MAT_A</A> </B></TD><TD> - first problem matrix obtained from Arnoldi
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B><A HREF="../DS/DSMatType.html#DSMatType">DS_MAT_B</A> </B></TD><TD> - second problem matrix obtained from Arnoldi on the transpose
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B><A HREF="../DS/DSMatType.html#DSMatType">DS_MAT_Q</A> </B></TD><TD> - orthogonal/unitary transformation that reduces A to Hessenberg form
(intermediate step) or matrix of orthogonal Schur vectors of A
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B><A HREF="../DS/DSMatType.html#DSMatType">DS_MAT_Z</A> </B></TD><TD> - orthogonal/unitary transformation that reduces B to Hessenberg form
(intermediate step) or matrix of orthogonal Schur vectors of B
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#883300">Implemented methods</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>0 </B></TD><TD> - Implicit QR (_hseqr)
</TD></TR></TABLE>
<P>
<H3><FONT COLOR="#883300">See Also</FONT></H3>
<A HREF="../DS/DSCreate.html#DSCreate">DSCreate</A>(), <A HREF="../DS/DSSetType.html#DSSetType">DSSetType</A>(), <A HREF="../DS/DSType.html#DSType">DSType</A>
<BR><P><B></B><H3><FONT COLOR="#883300">Level</FONT></H3>beginner<BR>
<H3><FONT COLOR="#883300">Location</FONT></H3>
</B><A HREF="../../../src/sys/classes/ds/impls/nhepts/dsnhepts.c.html#DSNHEPTS">src/sys/classes/ds/impls/nhepts/dsnhepts.c</A>
<BR><BR><A HREF="./index.html">Index of all DS routines</A>
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