Crouzeix's conjecture and perturbed Jordan blocks

DOI10.1016/j.laa.2011.12.005zbMath1390.15074OpenAlexW2079055561WikidataQ123308178 ScholiaQ123308178MaRDI QIDQ2427921

Daeshik Choi, Anne Greenbaum

Publication date: 19 April 2012

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2011.12.005

zbMATH Keywords

numerical rangefield of valuesCrouzeix's conjecture

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Miscellaneous inequalities involving matrices (15A45)

Related Items (9)

Variational analysis of the Crouzeix ratio ⋮ Pseudoeigenvector bases and deflated GMRES for highly nonnormal matrices ⋮ Between the von Neumann inequality and the Crouzeix conjecture ⋮ A proof of Crouzeix's conjecture for a class of matrices ⋮ Crouzeix's Conjecture Holds for Tridiagonal 3 x 3 Matrices with Elliptic Numerical Range Centered at an Eigenvalue ⋮ Crouzeix's conjecture and related problems ⋮ Numerical investigation of Crouzeix's conjecture ⋮ Curves of geodesic centers and Poncelet ellipses ⋮ Roots of Matrices in the Study of GMRES Convergence and Crouzeix's Conjecture

Uses Software

• Schwarz-Christoffel
• SC Toolbox

Cites Work

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• Numerical range and functional calculus in Hilbert space
• Upper and lower bounds on norms of functions of matrices
• Constants related to operators of class \(C_\rho\)
• Bounds for analytical functions of matrices
• Algorithm 756: a MATLAB toolbox for Schwarz-Christoffel mapping
• Eine Spektraltheorie für allgemeine Operatoren eines unitären Raumes. Erhard Schmidt zum 75. Geburtstag in Verehrung gewidmet

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