Explicit inverses of Toeplitz and associated matrices

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EXPLICIT EIGENVALUES AND INVERSES OF TRIDIAGONAL TOEPLITZ MATRICES WITH FOUR PERTURBED CORNERS (2008, background): “Toeplitz matrices are intimately related to boundary value problems involving difference equations, and the corresponding relations have been exploited in [2, 3] for ﬁnding inverses of matrices arising from difference operators.”
On the asymptotics of penalized splines (2008, unknown): “The inverses of such matrices have been much studied; see Dow (2003) for a review.”