resolvent_amplification.tex

Paper II: Refinement Towers, Weighted Transfer, and Integral Separation of Operator Packets

resolvent_amplification.tex

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1 \begin{tikzpicture}[x=1cm,y=1cm,>=Latex,font=\sffamily\small,line cap=round]
2 \node[anchor=east] at (-0.20000,4.03000) {$\frac{5}{2}$};
3 \draw[fill=black!65,draw=black!45,line width=.35pt,] (0.00000,3.80000) rectangle ++(0.10000,0.46000);
4 \node[anchor=west] at (0.30000,4.03000) {$\frac{4}{3}$};
5 \node[anchor=east] at (-0.20000,3.11000) {$\frac{11}{5}$};
6 \draw[fill=black!65,draw=black!45,line width=.35pt,] (0.00000,2.88000) rectangle ++(0.31250,0.46000);
7 \node[anchor=west] at (0.51250,3.11000) {$\frac{25}{6}$};
8 \node[anchor=east] at (-0.20000,2.19000) {$\frac{21}{10}$};
9 \draw[fill=black!65,draw=black!45,line width=.35pt,] (0.00000,1.96000) rectangle ++(0.68182,0.46000);
10 \node[anchor=west] at (0.88182,2.19000) {$\frac{100}{11}$};
11 \node[anchor=east] at (-0.20000,1.27000) {$\frac{41}{20}$};
12 \draw[fill=black!65,draw=black!45,line width=.35pt,] (0.00000,1.04000) rectangle ++(1.42857,0.46000);
13 \node[anchor=west] at (1.62857,1.27000) {$\frac{400}{21}$};
14 \node[anchor=east] at (-0.20000,0.35000) {$\frac{201}{100}$};
15 \draw[fill=black!65,draw=black!45,line width=.35pt,] (0.00000,0.12000) rectangle ++(7.42574,0.46000);
16 \node[anchor=west] at (7.62574,0.35000) {$\frac{10000}{101}$};
17 \node[anchor=east] at (-0.20000,4.65000) {$z$};
18 \node[] at (4.00000,4.65000) {$\|C R_f-R_c C\|_\infty/\varepsilon$};
19 \node[] at (4.70000,-1.15000) {Exact rational samples; the point $z=2$ itself is excluded.};
20 \end{tikzpicture}

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