Extended and Improved Criss-Cross Algorithms for Computing the Spectral Value Set Abscissa and Radius

DOI10.1137/19M1246213zbMath1457.93066arXiv1712.10067WikidataQ115214773 ScholiaQ115214773MaRDI QIDQ5203963

Tim Mitchell, Peter Benner

Publication date: 9 December 2019

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

Full work available at URL: https://arxiv.org/abs/1712.10067

zbMATH Keywords

robust stabilityHamiltonianstability radiuspseudospectrasymplecticH-infinity norm

Mathematics Subject Classification ID

(H^infty)-control (93B36) Linear systems in control theory (93C05) Robust stability (93D09)

Related Items (6)

Convergence Rate Analysis and Improved Iterations for Numerical Radius Computation ⋮ Fast computation of \(\mathrm{sep}_\lambda\) via interpolation-based globality certificates ⋮ Root-Max Problems, Hybrid Expansion-Contraction, and Quadratically Convergent Optimization of Passive Systems ⋮ Nearest \(\Omega \)-stable matrix via Riemannian optimization ⋮ Fast Interpolation-Based Globality Certificates for Computing Kreiss Constants and the Distance to Uncontrollability ⋮ Computing the Kreiss Constant of a Matrix

Uses Software

• SLICOT
• eigs
• ARPACK
• Eigtool
• Seigtool
• PSAPSR

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Singular control systems
• A structured pseudospectral method for \(\mathcal {H}_{\infty}\)-norm computation of large-scale descriptor systems
• On eigenvalues of matrices dependent on a parameter
• Large-Scale Computation of Pseudospectra Using ARPACK and Eigs
• Fast Approximation of the $H_\infty$ Norm via Optimization over Spectral Value Sets
• Hydrodynamic Stability Without Eigenvalues
• Mathematical Systems Theory I
• Fast Algorithms for the Approximation of the Pseudospectral Abscissa and Pseudospectral Radius of a Matrix
• A Bisection Method for Measuring the Distance of a Stable Matrix to the Unstable Matrices
• Stability radii of linear discrete‐time systems and symplectic pencils
• Robust stability and a criss-cross algorithm for pseudospectra
• Faster and More Accurate Computation of the $\mathcal{H}_\infty$ Norm via Optimization
• Hybrid expansion–contraction: a robust scaleable method for approximating theH_∞norm
• Second Derivatives for Optimizing Eigenvalues of Symmetric Matrices
• Algorithms for the computation of the pseudospectral radius and the numerical radius of a matrix

This page was built for publication: Extended and Improved Criss-Cross Algorithms for Computing the Spectral Value Set Abscissa and Radius