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.
THE STRUCTURED DISTANCE TO SINGULARITY OF A SYMMETRIC TRIDIAGONAL TOEPLITZ MATRIX / Noschese, S.. - In: ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS. - ISSN 1068-9613. - 59:(2023), pp. 43-59. [10.1553/etna_vol59s43]
THE STRUCTURED DISTANCE TO SINGULARITY OF A SYMMETRIC TRIDIAGONAL TOEPLITZ MATRIX
Noschese S.
2023
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.File allegati a questo prodotto
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