2014/01/02 by E. Kokabifar, Kokabifar, Esmaeil, Ghasem Barid Loghmani +5
Computer Science · Mathematics · #FOS: Mathematics #Graph theory and applications #Matrix Theory and Algorithms #Numerical Analysis (math.NA) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1401.0490
openalex publication_date 2014/01/02 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01
Consider an n × n matrix polynomial P(λ). A spectral norm distance from P(λ) to the set of n × n matrix polynomials that have a given scalar μ∈ℂ as a multiple eigenvalue was introduced and obtained by Papathanasiou and Psarrakos. They computed lower and upper bounds for this distance, constructing an associated perturbation of P(λ). In this paper, we extend this result to the case of two given distinct complex numbers μ1 and μ2. First, we compute a lower bound for the spectral norm distance from P(λ) to the set of matrix polynomials that have μ1,μ2 as two eigenvalues. Then we construct an associated perturbation of P(λ), such that the perturbed matrix polynomial has two given scalars μ1 and μ2 in its spectrum. Finally, we derive an upper bound for the distance by the constructed perturbation of P(λ). Numerical examples are provided to illustrate the validity of the method.