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Solving a block tridiagonal system with diagonal perturbations

Say we have a block tridiagonal matrix, $T \in \mathbb{R}^{NL \times NL}$, with constant off diagonals, $\mathbf{B} \in \mathbb{R}^{L\times L}$, given by $$ T = \begin{bmatrix} \mathbf{A}_1 & \...
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