The structured distance to singularity of a symmetric tridiagonal Toeplitz matrix

06/06/2022
by   Silvia Noschese, et al.
0

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.

READ FULL TEXT

page 5

page 12

research
04/12/2022

On the banded Toeplitz structured distance to symmetric positive semidefiniteness

This paper is concerned with the determination of a close real banded po...
research
06/14/2021

Optimizing Rayleigh quotient with symmetric constraints and their applications to perturbations of the structured polynomial eigenvalue problem

For a Hermitian matrix H ∈ℂ^n,n and symmetric matrices S_0, S_1,…,S_k ∈ℂ...
research
03/16/2022

A Structure-Preserving Divide-and-Conquer Method for Pseudosymmetric Matrices

We devise a spectral divide-and-conquer scheme for matrices that are sel...
research
02/01/2017

On the optimality and sharpness of Laguerre's lower bound on the smallest eigenvalue of a symmetric positive definite matrix

Lower bounds on the smallest eigenvalue of a symmetric positive definite...
research
03/06/2020

Updating structured matrix pencils with no spillover effect on unmeasured spectral data and deflating pair

This paper is devoted to the study of perturbations of a matrix pencil, ...
research
11/30/2018

Asymmetry Helps: Eigenvalue and Eigenvector Analyses of Asymmetrically Perturbed Low-Rank Matrices

This paper is concerned with a curious phenomenon in spectral estimation...
research
07/01/2017

Geometry-Oblivious FMM for Compressing Dense SPD Matrices

We present GOFMM (geometry-oblivious FMM), a novel method that creates a...

Please sign up or login with your details

Forgot password? Click here to reset