Abstract
We consider large finite Toeplitz matrices with symbols of the form (1− cos θ) p f(θ) where p is a natural number and f is a sufficiently smooth positive function. By employing techniques based on the use of predictor polynomials, we derive exact and asymptotic formulas for the entries of the inverses of these matrices. We show in particular that asymptotically the inverse matrix mimics the Green kernel of a boundary value problem for the differential operator \(( - 1)^p \frac{{d^{2p} }} {{dx^{2p} }}.\)
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