Generalization and variations of Pellet's theorem for matrix polynomials

Aaron Melman

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arXiv · 1210.0172

Generalization and variations of Pellet's theorem for matrix polynomials

Aaron Melman

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Abstract

We derive a generalized matrix version of Pellet's theorem, itself based on a generalized Rouché theorem for matrix-valued functions, to generate upper, lower, and internal bounds on the eigenvalues of matrix polynomials. Variations of the theorem are suggested to try and overcome situations where Pellet's theorem cannot be applied.

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Aaron Melman. 2013-02-15. Generalization and variations of Pellet's theorem for matrix polynomials. https://arxiv.org/abs/1210.0172

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