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<div id="version" align=right><b>petsc-3.10.3 2018-12-18</b></div>
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<A NAME="MATMFFD_DS"><H1>MATMFFD_DS</H1></A>
the code for compute the "h" used in the finite difference matrix-free matrix vector product. This code implements the strategy in Dennis and Schnabel, "Numerical Methods for Unconstrained Optimization and Nonlinear Equations".
<H3><FONT COLOR="#CC3333">Options Database Keys</FONT></H3>
<DT><B>-mat_mffd_umin <umin> see <A HREF="../Mat/MatMFFDDSSetUmin.html#MatMFFDDSSetUmin">MatMFFDDSSetUmin</A>()</B> -
<br>
<P>
<H3><FONT COLOR="#CC3333">Notes</FONT></H3>
Requires 2 norms and 1 inner product, but they are computed together
so only one parallel collective operation is needed. See <A HREF="../Mat/MATMFFD_WP.html#MATMFFD_WP">MATMFFD_WP</A> for a method
(with GMRES) that requires NO collective operations.
<P>
<H3><FONT COLOR="#CC3333">Formula used</FONT></H3>
F'(u)*a = [F(u+h*a) - F(u)]/h where
h = error_rel*u'a/||a||^2 if |u'a| > umin*||a||_{1}
= error_rel*umin*sign(u'a)*||a||_{1}/||a||^2 otherwise
where
error_rel = square root of relative error in function evaluation
umin = minimum iterate parameter
<P>
<H3><FONT COLOR="#CC3333">See Also</FONT></H3>
<A HREF="../Mat/MATMFFD.html#MATMFFD">MATMFFD</A>, <A HREF="../Mat/MatCreateMFFD.html#MatCreateMFFD">MatCreateMFFD</A>(), <A HREF="../SNES/MatCreateSNESMF.html#MatCreateSNESMF">MatCreateSNESMF</A>(), <A HREF="../Mat/MATMFFD_WP.html#MATMFFD_WP">MATMFFD_WP</A>, <A HREF="../Mat/MatMFFDDSSetUmin.html#MatMFFDDSSetUmin">MatMFFDDSSetUmin</A>()
<BR>
<P>
<P><B></B><H3><FONT COLOR="#CC3333">Level</FONT></H3>intermediate<BR>
<H3><FONT COLOR="#CC3333">Location</FONT></H3>
</B><A HREF="../../../src/mat/impls/mffd/mffddef.c.html#MATMFFD_DS">src/mat/impls/mffd/mffddef.c</A>
<P><H3><FONT COLOR="#CC3333">Examples</FONT></H3>
<A HREF="../../../src/snes/examples/tutorials/ex14.c.html">src/snes/examples/tutorials/ex14.c.html</A><BR>
<BR><A HREF="./index.html">Index of all Mat routines</A>
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