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arXiv · 1505.05931

Explicit Bounds for the Pseudospectra of Various Classes of Matrices and Operators

Feixue Gong·Olivia Meyerson·Jeremy Meza·Mihai Stoiciu·Abigail Ward
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Abstract

We study the $\epsilon$-pseudospectra $\sigma_\epsilon(A)$ of square matrices $A \in \mathbb{C}^{N \times N}$. We give a complete characterization of the $\epsilon$-pseudospectrum of any $2 \times 2$ matrix and describe the asymptotic behavior (as $\epsilon \to 0$) of $\sigma_\epsilon(A)$ for any square matrix $A$. We also present explicit upper and lower bounds for the $\epsilon$-pseudospectra of bidiagonal matrices, as well as for finite rank operators.

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Feixue Gong, Olivia Meyerson, Jeremy Meza, Mihai Stoiciu, Abigail Ward. 2015-05-22. Explicit Bounds for the Pseudospectra of Various Classes of Matrices and Operators. https://doi.org/10.2140/involve.2016.9.517

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