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Conference Papers Year : 2012

Tropical bounds for the eigenvalues of structured matrices

Abstract

We establish several inequalities of log-majorization type, relating the moduli of the eigenvalues of a complex matrix or matrix polynomial with the tropical eigenvalues of auxiliary matrix polynomials. This provides bounds which can be computed by combinatorial means. We consider in particular structured matrices and obtain bounds depending on the norms of block submatrices and on the pattern (graph structure) of the matrix.
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Dates and versions

hal-00782790 , version 1 (30-01-2013)

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  • HAL Id : hal-00782790 , version 1

Cite

Marianne Akian, Stéphane Gaubert, M. Sharify. Tropical bounds for the eigenvalues of structured matrices. 2012 SIAM Conference on Applied Linear Algebra, 2012, Valencia, Spain, Spain. ⟨hal-00782790⟩
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