Prescribed Eigenvalues via Optimal Perturbation of main-diagonal submatrix

2025/10/21 by M.R. Eslahchi, Eslahchi, M. R., E. Kokabifar +1
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Mathematics #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2510.18486

openalex publication_date 2025/10/21 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

Consider a given square matrix \textrm K with square blocks A₁₁,A₂₂,…,A_nn on the main diagonal. This paper aims to compute an optimal perturbation Δ of a preassigned block A_ii∈ℂ^{d_i× d_k}, (1≤ i≤ n),with respect to the spectral norm distance, such that the perturbed matrix \textrm K_X has k ≤ d_i prescribed eigenvalues. This paper presents a method for constructing the optimal perturbation by improving and extending the methodology, necessary definitions and lemmas of previous related works. Some conceivable applications of this subject are also presented. Numerical experiments are provided to illustrate the validity of the method.

Citations

• Measuring the stability of spectral clustering
• Nearest matrix with prescribed eigenvalues and its applications

Related

• Nearest matrix with prescribed eigenvalues and its applications
• Perturbation bounds of eigenvalues of Hermitian matrices with block structures
• First-order Perturbation Theory for Eigenvalues and Eigenvectors
• Perturbation of eigenvalues of matrix pencils and optimal assignment problem
• Determining the eigenvalues of a square matrix through known information of its submatrix