Optimizing the Spectral Radius

Optimizing the Spectral Radius

We suggest a new approach to finding the maximal and the minimal spectral radii of linear operators from a given compact family of operators, which share a common invariant cone (e.g., family of nonnegative matrices). In the case of families with the so-called product structure, this leads to effici...

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Veröffentlicht in:SIAM journal on matrix analysis and applications 2013-01, Vol.34 (3), p.999-1013
Hauptverfasser: Nesterov, Y., Protasov, V. Y.
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Difference equations
Eigenvectors
Grants
Graphs
Invariants
Linear operators
Operators
Optimization
Spectra
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Zusammenfassung:We suggest a new approach to finding the maximal and the minimal spectral radii of linear operators from a given compact family of operators, which share a common invariant cone (e.g., family of nonnegative matrices). In the case of families with the so-called product structure, this leads to efficient algorithms for optimizing the spectral radius and for finding the joint and lower spectral radii of the family. Applications to the theory of difference equations and to problems of optimizing the spectral radius of graphs are considered. [PUBLICATION ABSTRACT]
ISSN:0895-4798
1095-7162
DOI:10.1137/110850967