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<A NAME="KSPLSQR"><H1>KSPLSQR</H1></A>
This implements LSQR
<H3><FONT COLOR="#CC3333">Options Database Keys</FONT></H3>
<DT><B>see <A HREF="../KSP/KSPSolve.html#KSPSolve">KSPSolve</A>()</B> -
<br>
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<H3><FONT COLOR="#CC3333">Notes</FONT></H3>
This varient, when applied with no preconditioning is identical to the original algorithm in exact arithematic; however, in practice, with no preconditioning
due to inexact arithematic, it can converge differently. Hence when no preconditioner is used (<A HREF="../PC/PCType.html#PCType">PCType</A> <A HREF="../PC/PCNONE.html#PCNONE">PCNONE</A>) it automatically reverts to the original algorithm.
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With the PETSc built-in preconditioners, such as ICC, one should call <A HREF="../KSP/KSPSetOperators.html#KSPSetOperators">KSPSetOperators</A>(ksp,A,A'*A,...) since the preconditioner needs to work
for the normal equations A'*A.
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Supports only left preconditioning.
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References:The original unpreconditioned algorithm can be found in Paige and Saunders, ACM Transactions on Mathematical Software, Vol 8, pp 43-71, 1982.
In exact arithmetic the LSQR method (with no preconditioning) is identical to the <A HREF="../KSP/KSPCG.html#KSPCG">KSPCG</A> algorithm applied to the normal equations.
The preconditioned varient was implemented by Bas van't Hof and is essentially a left preconditioning for the Normal Equations.
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Developer Notes: How is this related to the <A HREF="../KSP/KSPCGNE.html#KSPCGNE">KSPCGNE</A> implementation? One difference is that <A HREF="../KSP/KSPCGNE.html#KSPCGNE">KSPCGNE</A> applies
the preconditioner transpose times the preconditioner, so one does not need to pass A'*A as the third argument to <A HREF="../KSP/KSPSetOperators.html#KSPSetOperators">KSPSetOperators</A>().
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<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>
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<P><B><P><B><FONT COLOR="#CC3333">Level:</FONT></B>beginner
<BR><FONT COLOR="#CC3333">Location:</FONT></B><A HREF="../../../src/ksp/ksp/impls/lsqr/lsqr.c.html#KSPLSQR">src/ksp/ksp/impls/lsqr/lsqr.c</A>
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