The extension of Weyl-type relative perturbation bounds

2023/08/19 by Haoyuan Ma, Ma, Haoyuan
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Mathematical Inequalities and Applications #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2308.09994

openalex publication_date 2023/08/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend several relative perturbation bounds to Hermitian matrices that are possibly singular, and also develop a general class of relative bounds for Hermitian matrices. As a result, corresponding relative bounds for singular values of rank-deficient m× n matrices are also obtained using the Jordan-Wielandt matrices. We also present that the main relative bound derived would be invariant with respect to congruence transformation under certain conditions, and compare its sharpness with the Weyl's absolute perturbation bound.

Related

• Combined perturbation bounds for eigenstructure of Hermitian matrices and singular structure of general matrices
• Random perturbation of low rank matrices: Improving classical bounds
• Relative Perturbation Bounds for the Joint Spectrum of Commuting Tuple of Matrices
• Perturbation bounds of eigenvalues of Hermitian matrices with block structures
• Relative perturbation bounds with applications to empirical covariance operators