Spectral Sets: Numerical Range and Beyond

DOI10.1137/18M1198417OpenAlexW2972658560WikidataQ127243662 ScholiaQ127243662MaRDI QIDQ5237900

Michel Crouzeix, Anne Greenbaum

Publication date: 25 October 2019

Published in: SIAM Journal on Matrix Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.10904

zbMATH Keywords

numerical rangespectral set

Mathematics Subject Classification ID

Norms (inequalities, more than one norm, etc.) of linear operators (47A30) Spectral sets of linear operators (47A25)

Related Items (4)

A note on a spectral constant associated with an annulus ⋮ Geometric dilations and operator annuli ⋮ Between the von Neumann inequality and the Crouzeix conjecture ⋮ Some uses of the field of values in numerical analysis

Uses Software

• RKToolbox

Cites Work

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• The annulus as a K-spectral set
• Intersections of several disks of the Riemann sphere as \(K\)-spectral sets
• Rational Krylov approximation of matrix functions: Numerical methods and optimal pole selection
• Error Estimates and Evaluation of Matrix Functions via the Faber Transform
• From Potential Theory to Matrix Iterations in Six Steps
• Extended Krylov Subspaces: Approximation of the Matrix Square Root and Related Functions
• Remarks on the Crouzeix--Palencia Proof that the Numerical Range is a (1+\sqrt2)-Spectral Set
• Some Extensions of the Crouzeix--Palencia Result
• Roots of Matrices in the Study of GMRES Convergence and Crouzeix's Conjecture
• The Numerical Range is a $(1+\sqrt{2})$-Spectral Set
• The analytic capacity of sets in problems of approximation theory

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