2025/12/04 by Kanhya, Prince, Raj, Udit
#FOS: Mathematics #Numerical Analysis (math.NA)
paper · doi:10.48550/arxiv.2512.04812
We study the problem of determining whether a prescribed eigenpair (λ,x) can be made an exact eigenpair of a nonnegative Hankel matrix through the smallest possible structured perturbation. The task reduces to check the feasibility of a set of linear constraints that encode both the Hankel structure and entrywise nonnegativity. When the feasibility set is nonempty, we compute the minimum-norm perturbation ΔH such that (H+ΔH)x=λx. When no such perturbation exists, we compute the nearest nonnegative Hankel matrix in a residual sense by minimizing ‖(H+ΔH)x-λx‖2 subject to the imposed constraints. Because closed-form formulas for the structured backward error are generally unavailable, our method provides a fully numerical and optimization-based framework for evaluating eigenpair sensitivity under nonnegativity-preserving Hankel perturbations. Numerical examples illustrate both feasible and infeasible cases.