对称三对角Toeplitz矩阵到奇异性的结构距离
The structured distance to singularity of a symmetric tridiagonal Toeplitz matrix
摘要：
本文研究了对称三对角Toeplitz矩阵$T$到相似结构奇异矩阵簇的距离，以及在这类矩阵簇中确定最接近$T$的矩阵.明确的公式，利用分析的灵敏度的频谱$T$相对于其条目的结构保持扰动。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
