Nearest matrix with prescribed eigenvalues and its applications

Consider an n×n matrix A and a set Λ consisting of k≤n prescribed complex numbers. Lippert (2010) in a challenging article, studied geometrically the spectral norm distance from A to the set of matrices whose spectra included specified set Λ and constructed a perturbation matrix Δ with minimum spect...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2016-05, Vol.298, p.53-63
Main Authors: Kokabifar, E., Loghmani, G.B., Karbassi, S.M.
Format: Article
Language:English
Subjects:
Computation
Eigenvalue
Eigenvalues
Mathematical analysis
Matrices (mathematics)
Matrix
Norms
Optimization
Perturbation
Perturbation methods
Singular value
Spectra
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Summary:Consider an n×n matrix A and a set Λ consisting of k≤n prescribed complex numbers. Lippert (2010) in a challenging article, studied geometrically the spectral norm distance from A to the set of matrices whose spectra included specified set Λ and constructed a perturbation matrix Δ with minimum spectral norm such that A+Δ had Λ in its spectrum. This paper presents an easy practical computational method for constructing the optimal perturbation Δ by improving and extending the methodology, necessary definitions and lemmas of previous related works. Also, some conceivable applications of this issue are provided.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2015.11.031