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

2014/10/12 by Kokabifar, E., Loghmani, G. B., Psarrakos, P. J.
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.1410.3082

Abstract

Consider an n × n matrix polynomial P(λ). An upper bound for 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 recently obtained by Papathanasiou and Psarrakos (2008). This paper concerns a refinement of this result for the case of weakly normal matrix polynomials. A modification method is implemented and its efficiency is verified by an illustrative example.

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