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<A NAME="KSPCGNE"><H1>KSPCGNE</H1></A>
Applies the preconditioned conjugate gradient method to the normal equations without explicitly forming A^t*A
<H3><FONT COLOR="#CC3333">Options Database Keys</FONT></H3>
<DT><B>-ksp_cg_type <Hermitian or symmetric </B> -(for complex matrices only) indicates the matrix is Hermitian or symmetric
<br>
<P>
<P>
<P>
Notes: eigenvalue computation routines will return information about the
spectrum of A^t*A, rather than A.
<P>
This is NOT a different algorithm then used with <A HREF="../KSP/KSPCG.html#KSPCG">KSPCG</A>, it merely uses that algorithm with the
matrix defined by A^t*A and preconditioner defined by B^t*B where B is the preconditioner for A.
<P>
This method requires that one be apply to apply the transpose of the preconditioner and operator
as well as the operator and preconditioner. If the transpose of the preconditioner is not available then
the preconditioner is used in its place so one ends up preconditioning A'A with B B. Seems odd?
<P>
This only supports left preconditioning.
<P>
Developer Notes: How is this related to the preconditioned LSQR implementation?
<P>
This object is subclassed off of <A HREF="../KSP/KSPCG.html#KSPCG">KSPCG</A>
<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/KSPCGSetType.html#KSPCGSetType">KSPCGSetType</A>(), <A HREF="../KSP/KSPBICG.html#KSPBICG">KSPBICG</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/cg/cgne/cgne.c.html#KSPCGNE">src/ksp/ksp/impls/cg/cgne/cgne.c</A>
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