Paper VIII: Packet Operator Algorithms, Exact Compilation, and GPU Realization

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Stealth,line cap=round,line join=round]
2 \path[use as bounding box] (0,-.6) rectangle (14,4.8);
3 \node[font=\small,align=center,font=\small] at (1.65,4.5) {one block of $D^{-1}$};
4 \path[draw=black!30,fill=black!8] (0.8,2.95) rectangle (1.65,3.8);
5 \node[font=\small,align=center,font=\small] at (1.225,3.375) {$\frac{3}{8}$};
6 \path[draw=black!30,fill=black!8] (1.65,2.95) rectangle (2.5,3.8);
7 \node[font=\small,align=center,font=\small] at (2.075,3.375) {$- \frac{1}{8}$};
8 \path[draw=black!30,fill=black!8] (0.8,2.1) rectangle (1.65,2.95);
9 \node[font=\small,align=center,font=\small] at (1.225,2.525) {$- \frac{1}{8}$};
10 \path[draw=black!30,fill=black!8] (1.65,2.1) rectangle (2.5,2.95);
11 \node[font=\small,align=center,font=\small] at (2.075,2.525) {$\frac{3}{8}$};
12 \node[font=\small,align=center] at (6.25,3.5) {$D^{-1}u=\tfrac14 u$};
13 \node[font=\small,align=center] at (6.25,2.25) {$S=1+u^TD^{-1}u=\tfrac52$};
14 \node[font=\small,align=center] at (6.25,0.9) {$A^{-1}=D^{-1}-\tfrac1{40}uu^T$};
15 \node[font=\small,align=center,font=\small] at (11.45,4.25) {$I-e_1e_1^T$};
16 \path[draw=black!30,fill=white] (10.6,2.7) rectangle (11.45,3.55);
17 \node[font=\small,align=center,font=\small] at (11.025,3.125) {$0$};
18 \path[draw=black!30,fill=white] (11.45,2.7) rectangle (12.3,3.55);
19 \node[font=\small,align=center,font=\small] at (11.875,3.125) {$0$};
20 \path[draw=black!30,fill=white] (10.6,1.85) rectangle (11.45,2.7);
21 \node[font=\small,align=center,font=\small] at (11.025,2.275) {$0$};
22 \path[draw=black!30,fill=black!8] (11.45,1.85) rectangle (12.3,2.7);
23 \node[font=\small,align=center,font=\small] at (11.875,2.275) {$1$};
24 \node[font=\small,align=center,font=\scriptsize] at (11.45,0.7) {invertible $D$\\singular update};
25 \end{tikzpicture}

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