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<div id="version" align=right><b>petsc-3.4.2 2013-07-02</b></div>
<A NAME="SNESQN"><H1>SNESQN</H1></A>
Limited-Memory Quasi-Newton methods for the solution of nonlinear systems.
<H3><FONT COLOR="#CC3333">Options Database</FONT></H3>
<P>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-snes_qn_m </B></TD><TD>- Number of past states saved for the L-Broyden methods.
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-snes_qn_powell_angle </B></TD><TD>- Angle condition for restart.
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-snes_qn_powell_descent </B></TD><TD>- Descent condition for restart.
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-snes_linesearch_type <cp, l2, basic> </B></TD><TD>- Type of line search.
</TD></TR>
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-snes_qn_monitor </B></TD><TD>- Monitors the quasi-newton jacobian.
</TD></TR></TABLE>
<P>
Notes: This implements the L-BFGS, Broyden, and "Bad" Broyden algorithms for the solution of F(x) = b using
previous change in F(x) and x to form the approximate inverse Jacobian using a series of multiplicative rank-one
updates.
<P>
When using a nonlinear preconditioner, one has two options as to how the preconditioner is applied. The first of
these options, sequential, uses the preconditioner to generate a new solution and function and uses those at this
iteration as the current iteration's values when constructing the approximate jacobian. The second, composed,
perturbs the problem the jacobian represents to be P(x, b) - x = 0, where P(x, b) is the preconditioner.
<P>
<H3><FONT COLOR="#CC3333">References</FONT></H3>
<P>
L-Broyden Methods: a generalization of the L-BFGS method to the limited memory Broyden family, M. B. Reed,
International Journal of Computer Mathematics, vol. 86, 2009.
<P>
Experiments with Quasi-Newton Methods in Solving Stiff ODE Systems, Peter N. Brown, Alan C. Hindmarsh, Homer F. Walker
SIAM J. Sci. Stat. Comput. Vol 6(2), April 1985.
<P>
<P>
<P>
<H3><FONT COLOR="#CC3333">See Also</FONT></H3>
<A HREF="../SNES/SNESCreate.html#SNESCreate">SNESCreate</A>(), <A HREF="../SNES/SNES.html#SNES">SNES</A>, <A HREF="../SNES/SNESSetType.html#SNESSetType">SNESSetType</A>(), <A HREF="../SNES/SNESNEWTONLS.html#SNESNEWTONLS">SNESNEWTONLS</A>, <A HREF="../SNES/SNESNEWTONTR.html#SNESNEWTONTR">SNESNEWTONTR</A>
<BR>
<P>
<P><B><P><B><FONT COLOR="#CC3333">Level:</FONT></B>beginner
<BR><FONT COLOR="#CC3333">Location:</FONT></B><A HREF="../../../src/snes/impls/qn/qn.c.html#SNESQN">src/snes/impls/qn/qn.c</A>
<BR><A HREF="./index.html">Index of all SNES routines</A>
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