# Pseudospectra and Spectral Values Sets of Nonsymmetric Matrices

N. Guglielmi, M. Gürbüzbalaban, T. Mitchell and M.L. Overton,

** Approximating the Real Structured Stability Radius with Frobenius Norm Bounded Perturbations**

SIAM J. Matrix Anal. Appl., 38 (2017), pp. 1323–1353.

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T. Mitchell and M.L. Overton,

** Hybrid Expansion-Contraction: a Robust Scaleable Method for Approximating the H**_{∞} Norm

IMA J. Numer. Anal., 2015, doi: 10.1093/imanum/drv046

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N. Guglielmi, M. Gürbüzbalaban and M.L. Overton,

** Fast Approximation of the H**_{∞} Norm via Optimization over Spectral Value Sets

SIAM J. Matrix Anal. Appl. 34 (2013), pp. 709-737

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M. Gürbüzbalaban and M.L. Overton,

** Some Regularity Results for the Pseudospectral Abscissa and Pseudospectral Radius of a Matrix**

SIAM J. Optimization 22 (2012), pp. 281-285

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N. Guglielmi and M.L. Overton,

** Fast Algorithms for the Approximation of the Pseudospectral Abscissa and
Pseudospectral Radius of a Matrix**

SIAM J. Matrix Anal. Appl. 32 (2011), pp. 1166-1192

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R. Alam, S. Bora, R. Byers and M.L. Overton,

** Characterization and Construction of the Nearest Defective Matrix
via Coalescence of Pseudospectral Components**

* Linear Algebra and its Applications* 435 (2011), pp. 494-513

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J.V. Burke, A.S. Lewis and M.L. Overton,

** Spectral Conditioning and Pseudospectral Growth**

*Numerische Mathematik* 107 (2007), pp. 27-37

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J.V. Burke, A.S. Lewis and M.L. Overton,

** Convexity and Lipschitz Behavior of Small Pseudospectra**

* SIAM J. Matrix Anal. Appl.* 29 (2007), pp. 586-595

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M. Gu and M.L. Overton,

** An Algorithm to Compute Sep_Lambda**

* SIAM J. Matrix Anal. Appl.* 28 (2006), pp. 348-359

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E. Mengi and M.L. Overton,

** Algorithms for the Computation of the Pseudospectral Radius and the Numerical
Radius of a Matrix**

* IMA Journal of Numerical Analysis* 25 (2005) pp. 648-669

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J.V. Burke, A.S. Lewis and M.L. Overton,

** Pseudospectral Components and the Distance to Uncontrollability**

* SIAM J. Matrix Anal. Appl.* 26 (2004), pp. 350-361

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J.V. Burke, A.S. Lewis and M.L. Overton,

** A Nonsmooth, Nonconvex Optimization Approach to Robust Stabilization by
Static Output Feedback and Low-Order Controllers**

In: S.Bittanti and P. Colaneri, eds., Proceedings of Fourth IFAC Symposium on
Robust Control Design, Milan, June 2003, pp. 175-181 (Elsevier, 2004)

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Individual figures and problem data

J.V. Burke, A.S. Lewis and M.L. Overton,

** Robust Stability and A Criss-Cross Algorithm for Pseudospectra**

* IMA Journal of Numerical Analysis* 23 (2003), pp. 359-375.

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J.V. Burke, A.S. Lewis and M.L. Overton,

** Optimization and Pseudospectra, with Applications to Robust Stability**

* SIAM J. Matrix Anal. Appl.* 25 (2003), pp. 80-104.

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Corrigendum

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