Controlled approximation for the inverses of special tridiagonal Toeplitz and modified Toeplitz matrices

In this paper properties of monotone increasing behavior along the diagonals are exhibited for special classes of Toeplitz and modified Toeplitz matrices. By exploiting these properties, approximations are proposed for the inverses of these matrices, which have a large number of zero diagonals. An in-depth analysis is performed about the approximation level obtainable correspondingly to the number of diagonals set to zero. An application of the results in the context of optimal control is presented to show the advantage achievable by the proposed approximation with respect to the amount of information required.