Extrap: added info on Anderson mixing

Research/Extrapolation methods/notes.tex

@@ -525,4 +525,10 @@ If $\vec{v}_n$ is chosen such that
 \end{equation*}
 with possibly other constraints then $\hat{J}_{n+1} X_{n-k,k} \Delta = F_{n-k,k} \Delta$.
 
+Anderson mixing solves $F_{n,k} \Delta \vec{u} = \fxi{n+k}$ in a least-squares sense then uses the step
+\begin{equation*}
+\hat{\vec{x}}_{n+k+1} = \vec{x}_{n+k} - X_{n,k} \Delta \vec{u} + \beta \left ( \fxi{n+k} - F_{n,k} \Delta \vec{u} \right ).
+\end{equation*}
+For $\beta=0$ this is exactly the multisecant equations.
+
 \end{document}
\ No newline at end of file