What's the best way to invert a simple symmetric tridiagonal Toeplitz matrix of the following form?
$$ A = \begin{bmatrix} 1 & a & 0 & \ldots & \ldots & 0 \\\ a & 1 & a & \ddots & & \vdots \\\ 0 & a & 1 & \ddots & \ddots& \vdots \\\ \vdots & \ddots & \ddots & \ddots & a & 0\\\ \vdots & & \ddots & a & 1 & a\\\ 0 & \ldots & \ldots & 0 & a & 1 \end{bmatrix} $$