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Dominant eigenvalue minimization with trace preserving diagonal perturbation: Subset design problem | IEEE Conference Publication | IEEE Xplore

Dominant eigenvalue minimization with trace preserving diagonal perturbation: Subset design problem


Abstract:

We study the problem of minimizing the dominant eigenvalue of an essentially-nonnegative matrix with respect to a trace-preserving or fixed-trace diagonal perturbation, i...Show More

Abstract:

We study the problem of minimizing the dominant eigenvalue of an essentially-nonnegative matrix with respect to a trace-preserving or fixed-trace diagonal perturbation, in the case where only a subset of the diagonal entries can be perturbed. The spectrum of the perturbed matrix at the optimum is characterized. A constructive algorithm for computing the optimal diagonal trace-preserving perturbation is developed, using the spectral result together with line-sum-symmetrization arguments. A number of graph-theoretic results are developed on the optimal perturbation and how it changes if further entries are constrained, in part using properties of the Perron complement of nonnegative matrices.
Date of Conference: 15-18 December 2015
Date Added to IEEE Xplore: 11 February 2016
ISBN Information:
Conference Location: Osaka, Japan

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