Commit 27113bb0 authored by Conor McCoid's avatar Conor McCoid
Browse files

Extrap: reduced width of map of methods

parent a400f4a1
......@@ -610,26 +610,25 @@ If one minimizes with respect to a different norm then the methods correspond to
\begin{figure}
\centering
\begin{tikzpicture}
\matrix (m) [column sep=2cm, row sep=1em]{
\node[align=left] (multisecant) {$\begin{bmatrix} \vec{1}^\top \\ F_{n,k} \end{bmatrix} \vec{u} = \begin{bmatrix} 1 \\ 0 \end{bmatrix}$,\\ $X_{n,k} \vec{u} = \hat{\vec{x}}$}; &
\node (overdetermined) {$\begin{bmatrix} \vec{1}^\top \\ B^\top F_{n,k} \end{bmatrix} \vec{u} = \begin{bmatrix} 1 \\ 0 \end{bmatrix}$}; &
\node (preMPE) {}; &
\node (Anderson) {Anderson mixing}; \\
& & & \node (MPE) {MPE}; \\
\matrix (m) [column sep=1cm, row sep=1em]{
& & & & \node[align=left] (Anderson) {Anderson\\mixing}; \\
\node[align=left] (multisecant) {$\begin{bmatrix} \vec{1}^\top \\ F_{n,k} \end{bmatrix} \vec{u} = \begin{bmatrix} 1 \\ 0 \end{bmatrix}$,\\ $X_{n,k} \vec{u} = \hat{\vec{x}}$}; &
\node (overdetermined) {$\begin{bmatrix} \vec{1}^\top \\ B^\top F_{n,k} \end{bmatrix} \vec{u} = \begin{bmatrix} 1 \\ 0 \end{bmatrix}$}; & &
\node (preMPE) {}; & \node (MPE) {MPE}; \\
& & & & \node (GMRES) {GMRES}; \\
\node[align=left] (preBroyden) {$\begin{bmatrix} \vec{1}^\top & \vec{1}^\top \\ F_{n,k} & B \end{bmatrix} \vec{u} = \begin{bmatrix} 1 \\ 0 \end{bmatrix}$,\\ $\begin{bmatrix} X_{n,k} & C \end{bmatrix} \vec{u} = \hat{\vec{x}}$};
& & & \node (GMRES) {GMRES}; \\
& \node (prepreRRE) {}; & \node (preRRE) {}; & \node (RRE) {RRE}; \\
& & & \node (GCR) {GCR}; \\
& \node (prepreMMPE) {}; & \node (preMMPE) {}; & \node (MMPE) {MMPE}; \\
& \node (prepreRRE) {}; & & \node (preRRE) {}; & \node (RRE) {RRE}; \\
& & & & \node (GCR) {GCR}; \\
& \node (prepreMMPE) {}; & & \node (preMMPE) {}; & \node (MMPE) {MMPE}; \\
& \node (preTEA) {}; & & \node (preBiCG) {}; & \node (BiCG) {BiCG}; \\
\node (Broyden) {Generalized Broyden};
& \node (preTEA) {}; & \node (preBiCG) {}; & \node (BiCG) {BiCG}; \\
& & & \node (TEA) {TEA}; \\
& & & & \node (TEA) {TEA*}; \\
};
\path[->,very thick]
(multisecant) edge node[above] {$k \neq d$} (overdetermined) edge node[right] {$k < d$} (preBroyden)
(preBroyden) edge node[right,align=left] {$(C \Delta)^\top (X_{n,k} \Delta) = 0$, \\ $B = \hat{J}_{n-1,k} C$} (Broyden)
(overdetermined) edge node[above] {$B=F_{n,k-1}$} (preMPE)
(preMPE) edge node[above] {+ relaxation} (Anderson)
(preMPE) edge[red] (MPE)
(prepreRRE) edge node[above] {$B=F_{n,k} \Delta$} (preRRE)
(preRRE) edge[red] (RRE)
(prepreMMPE) edge node[above] {$B=\begin{bmatrix} \vec{q}_1 & \dots & \vec{q}_k \end{bmatrix}$} (preMMPE)
......@@ -638,12 +637,13 @@ If one minimizes with respect to a different norm then the methods correspond to
(preBiCG) edge[blue] (BiCG)
(BiCG) edge[red] (TEA);
\draw[-, very thick] (overdetermined) edge (preTEA);
\draw[->,very thick,red] (preMPE) |- (MPE);
\draw[->,very thick,blue] (preMPE) |- (GMRES);
\draw[->,very thick,blue] (preRRE) |- (GCR);
\draw[->,very thick] (preMPE) |- node[above] {+relaxation} (Anderson);
\end{tikzpicture}
\caption{Interconnectivity of extrapolation, acceleration and quasi-Newton methods.
Red arrows indicated $\fxi{n} = \vec{x}_{n+1}-\vec{x}_n$ while blue arrows indicate $\fxi{n} = (A-I) \vec{x}_n + \vec{b}$ and $\fxi{n+1} = A \fxi{n}$.}
Red arrows indicated $\fxi{n} = \vec{x}_{n+1}-\vec{x}_n$ while blue arrows indicate $\fxi{n} = (A-I) \vec{x}_n + \vec{b}$ and $\fxi{n+1} = A \fxi{n}$.
Note that TEA* is the linear version of the method; general TEA derives directly from the multisecant equations.}
\end{figure}
\end{document}
\ No newline at end of file
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