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Upper bound for $\|\textbf{D}^{-1}\|$, where $\textbf{D}$ is a matrix with specific sparse pattern

Consider the block matrix given by $$\textbf{D} = \left[ \begin{array}{ccc} \left[ \begin{array}{ccc} D & \ldots & D\\ \vdots & \ddots & \vdots\\ D &...
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