Numerical investigation of Crouzeix's conjecture

DOI10.1016/j.laa.2017.04.035zbMath1415.15021OpenAlexW2611283298WikidataQ123190030 ScholiaQ123190030MaRDI QIDQ2002781

Michael L. Overton, Anne Greenbaum

Publication date: 12 July 2019

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

Full work available at URL: https://doi.org/10.1016/j.laa.2017.04.035

zbMATH Keywords

nonsmooth optimizationnumerical rangefield of values

Mathematics Subject Classification ID

Norms of matrices, numerical range, applications of functional analysis to matrix theory (15A60) Applications of operator theory in optimization, convex analysis, mathematical programming, economics (47N10)

Related Items (8)

Variational analysis of the Crouzeix ratio ⋮ On the uniqueness of functions that maximize the Crouzeix ratio ⋮ The Numerical Range is a $(1+\sqrt{2})$-Spectral Set ⋮ Convergence Rate Analysis and Improved Iterations for Numerical Radius Computation ⋮ Crouzeix's conjecture and related problems ⋮ Partial Smoothness of the Numerical Radius at Matrices Whose Fields of Values are Disks ⋮ Characterization of half-radial matrices ⋮ Local minimizers of the Crouzeix ratio: a nonsmooth optimization case study

Uses Software

• GradSamp
• Chebfun

Cites Work

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• Convergence of the Gradient Sampling Algorithm for Nonsmooth Nonconvex Optimization
• Numerical Determination of the Field of Values of a General Complex Matrix
• Roots of Matrices in the Study of GMRES Convergence and Crouzeix's Conjecture
• A Robust Gradient Sampling Algorithm for Nonsmooth, Nonconvex Optimization
• The Numerical Range is a $(1+\sqrt{2})$-Spectral Set
• On the numerical range of a matrix
• On a method of solving the complete eigenvalue problem for a degenerate matrix

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