Volume 59, pp. 43-59, 2023.

The structured distance to singularity of a symmetric tridiagonal Toeplitz matrix

Silvia Noschese

Abstract

This paper is concerned with the distance of a symmetric tridiagonal Toeplitz matrix $T$ to the manifold of similarly structured singular matrices, and with determining the closest matrix to $T$ in this manifold. Explicit formulas are presented, exploiting the analysis of the sensitivity of the spectrum of $T$ with respect to structure-preserving perturbations of its entries.

Full Text (PDF) [553 KB], BibTeX

Key words

matrix nearness problem, distance to singularity, eigenvalue conditioning, symmetric tridiagonal Toeplitz structure, structured distance

AMS subject classifications

65F15, 65F35, 15A12, 15A57

Links to the cited ETNA articles

[28]	Vol. 33 (2008-2009), pp. 63-83 Lothar Reichel and Qiang Ye: Simple square smoothing regularization operators

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