The structured distance to singularity of a symmetric tridiagonal Toeplitz matrix
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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.
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