On the distance from a matrix polynomial to matrix polynomials with some prescribed eigenvalues

On the distance from a matrix polynomial to matrix polynomials with two prescribed eigenvalues

Consider an n × <span style="fon...

on the distance from a matrix polynomial to matrix polynomials with two prescribed eigenvalues

consider an n × n matrix polynomial p(λ). a spectral norm distance from p(λ) to the set of n × n matrix polynomials that havea given scalar µ ∈ c as a multiple eigenvalue was introducedand obtained by papathanasiou and psarrakos. they computedlower and upper bounds for this distance, constructing an associated perturbation of p(λ). in this paper, we extend this resultto the case of two given di...

The distance from a matrix polynomial to matrix polynomials with a prescribed multiple eigenvalue

For a matrix polynomial P (λ) and a given complex number μ, we introduce a (spectral norm) distance from P (λ) to the matrix polynomials that have μ as an eigenvalue of geometric multiplicity at least κ, and a distance from P (λ) to the matrix polynomials that have μ as a multiple eigenvalue. Then we compute the first distance and obtain bounds for the second one, constructing associated pertur...

On the distance from a weakly normal matrix polynomial to matrix polynomials with a prescribed multiple eigenvalue

On robust matrix completion with prescribed eigenvalues

Matrix completion with prescribed eigenvalues is a special kind of inverse eigenvalue problems. Thus far, only a handful of specific cases concerning its existence and construction have been studied in the literature. The general problem where the prescribed entries are at arbitrary locations with arbitrary cardinalities proves to be challenging both theoretically and computationally. This pape...