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 \draw[black!13,line width=.25pt] (1.725,0.75) -- (1.725,3.85);
4 \draw[] (1.725,0.69) -- (1.725,0.81);
5 \node[font=\small,align=center,font=\scriptsize] at (1.725,0.49) {-1};
6 \draw[black!13,line width=.25pt] (3.275,0.75) -- (3.275,3.85);
7 \draw[] (3.275,0.69) -- (3.275,0.81);
8 \node[font=\small,align=center,font=\scriptsize] at (3.275,0.49) {0};
9 \draw[black!13,line width=.25pt] (4.825,0.75) -- (4.825,3.85);
10 \draw[] (4.825,0.69) -- (4.825,0.81);
11 \node[font=\small,align=center,font=\scriptsize] at (4.825,0.49) {1};
12 \draw[black!13,line width=.25pt] (0.95,1.266667) -- (5.6,1.266667);
13 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (0.79,1.266667) {-1};
14 \draw[black!13,line width=.25pt] (0.95,2.3) -- (5.6,2.3);
15 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (0.79,2.3) {0};
16 \draw[black!13,line width=.25pt] (0.95,3.333333) -- (5.6,3.333333);
17 \node[font=\small,align=center,anchor=east,font=\scriptsize] at (0.79,3.333333) {1};
18 \draw[->,line width=.6pt] (0.95,0.75) -- (5.72,0.75);
19 \draw[->,line width=.6pt] (0.95,0.75) -- (0.95,3.97);
20 \node[font=\small,align=center,font=\scriptsize] at (3.275,0.2) {packet 1};
21 \node[font=\small,align=center,anchor=west,font=\scriptsize] at (0.95,4.25) {packet 2};
22 \draw[line width=1.1pt] plot coordinates {(1.26,0.956667) (5.29,3.643333)};
23 \node[font=\small,align=center] at (3.25,4.25) {$A=I_2,\ v=(1,1)^T$};
24 \node[font=\small,align=center] at (9.5,3.3) {$p(A)v=p(1)(1,1)^T$};
25 \node[font=\small,align=center] at (9.5,2.1) {$\dim\mathcal K_m(A,v)=1$};
26 \node[font=\small,align=center] at (9.5,0.9) {Independent local spans have dimension $2$.};
27 \end{tikzpicture}

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