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 spectrum of $T$ with respect to structure-preserving perturbations of its entries.

翻译：本文研究了对称三对角Toeplitz矩阵$T$到同样结构化奇异矩阵多项式的距离，并确定了在该多项式中距离$T$最近的矩阵。提供了显式的公式，利用分析$T$的谱对保持结构的分量的扰动的灵敏度。