The structured distance to singularity of a symmetric tridiagonal Toeplitz matrix

This paper is concerned with the distance of a symmetric tridiagonal Toeplitz matrix $T$ to the variety of similarly structured singular matrices, and with determining the closest matrix to $T$ in this variety. Explicit formulas are presented, that exploit the analysis of the sensitivity of the smallest eigenvalue in magnitude of $T$ with respect to structure-preserving perturbations of its entries. Also, in case $T$ is positive definite, monotonicity properties of the entries of its Cholesky factor are shown.