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This paper is concerned with the determination of a close real bandedpositive definite Toeplitz matrix in the Frobenius norm to a given square realbanded matrix. While it is straightforward to determine the closest bandedToeplitz matrix to a given square matrix, the additional requirement ofpositive definiteness makes the problem difficult. We review availabletheoretical results and provide a simple approach to determine a bandedpositive definite Toeplitz matrix.

On the banded Toeplitz structured distance to symmetric positive semidefiniteness