circulant.tex

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 (2.16,4.4) {$C(c)$};
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35 \node[font=\small,align=center,font=\small] at (3.255,1.145) {$2$};
36 \node[font=\small,align=center,font=\small] at (5.675,4.4) {$\sqrt4\,Fc$};
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44 \node[font=\small,align=center,font=\small] at (5.675,1.145) {$2 + 2 i$};
45 \node[font=\small,align=center] at (10.7,3.4) {$F_{jk}=\frac12\,\mathrm i^{-jk}$};
46 \node[font=\small,align=center] at (10.7,2.2) {$C=F^*\diag(\sqrt4 Fc)F$};
47 \node[font=\small,align=center] at (10.7,1) {$\sqrt4=2$ is essential.};
48 \node[font=\small,align=center,font=\scriptsize] at (7,0.05) {A unitary transform changes the normalization of the convolution eigenvalues.};
49 \end{tikzpicture}

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