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<div id="version" align=right><b>petsc-3.4.2 2013-07-02</b></div>
<A NAME="SNESNRICHARDSON"><H1>SNESNRICHARDSON</H1></A>
Richardson nonlinear solver that uses successive substitutions, also sometimes known as Picard iteration.
<P>
<H3><FONT COLOR="#CC3333">Options Database</FONT></H3>
<TABLE border="0" cellpadding="0" cellspacing="0">
<TR><TD WIDTH=40></TD><TD ALIGN=LEFT VALIGN=TOP><B>-snes_linesearch_type <l2,cp,basic> Line search type.</B></TD><TD>- - -snes_linesearch_damping<1.0> Damping for the line search.
</TD></TR>
<P>
Notes: If no inner nonlinear preconditioner is provided then solves F(x) - b = 0 using x^{n+1} = x^{n} - lambda
(F(x^n) - b) where lambda is obtained either <A HREF="../SNES/SNESLineSearchSetDamping.html#SNESLineSearchSetDamping">SNESLineSearchSetDamping</A>(), -snes_damping or a line search. If
an inner nonlinear preconditioner is provided (either with -npc_snes_type or <A HREF="../SNES/SNESSetPC.html#SNESSetPC">SNESSetPC</A>()) then the inner
solver is called an initial solution x^n and the nonlinear Richardson uses x^{n+1} = x^{n} + lambda d^{n}
where d^{n} = \hat{x}^{n} - x^{n} where \hat{x}^{n} is the solution returned from the inner solver.
<P>
The update, especially without inner nonlinear preconditioner, may be ill-scaled. If using the basic
linesearch, one may have to scale the update with -snes_linesearch_damping
<P>
This uses no derivative information thus will be much slower then Newton's method obtained with -snes_type ls
<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>, <A HREF="../SNES/SNESNGMRES.html#SNESNGMRES">SNESNGMRES</A>, <A HREF="../SNES/SNESQN.html#SNESQN">SNESQN</A>, <A HREF="../SNES/SNESNCG.html#SNESNCG">SNESNCG</A>
<BR><P><B><P><B><FONT COLOR="#CC3333">Level:</FONT></B>beginner
<BR><FONT COLOR="#CC3333">Location:</FONT></B><A HREF="../../../src/snes/impls/richardson/snesrichardson.c.html#SNESNRICHARDSON">src/snes/impls/richardson/snesrichardson.c</A>
<BR><A HREF="./index.html">Index of all SNES routines</A>
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