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