On the Method by Rostami for Computing the Real Stability Radius of Large and Sparse Matrices

DOI10.1137/15M1029709zbMath1339.65053MaRDI QIDQ2811993

Nicola Guglielmi

Publication date: 10 June 2016

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

algorithmnumerical examplesiterative methodquadratic convergencefast methodslarge sparse matricesreal stability radiusLyapunov inverse iterationreal pseudospectral abscissareal pseudospectrum

Mathematics Subject Classification ID

Computational methods for sparse matrices (65F50) Numerical computation of eigenvalues and eigenvectors of matrices (65F15) Iterative numerical methods for linear systems (65F10)

Related Items (4)

On the real stability radius of sparse systems ⋮ Approximating the Real Structured Stability Radius with Frobenius-Norm Bounded Perturbations ⋮ Criss-Cross Type Algorithms for Computing the Real Pseudospectral Abscissa ⋮ Rank-1 Matrix Differential Equations for Structured Eigenvalue Optimization.

Uses Software

• MatrixMarket
• ARPACK
• Eigtool
• Seigtool
• PSAPSR

Cites Work

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• A new approach for calculating the real stability radius
• On the computation of structured singular values and pseudospectra
• Perturbation theory for linear operators.
• A formula for computation of the real stability radius
• Low rank differential equations for Hamiltonian matrix nearness problems
• Subspace Methods for Computing the Pseudospectral Abscissa and the Stability Radius
• Approximating real stability radii
• Mathematical Systems Theory I
• Fast Algorithms for the Approximation of the Pseudospectral Abscissa and Pseudospectral Radius of a Matrix
• New Algorithms for Computing the Real Structured Pseudospectral Abscissa and the Real Stability Radius of Large and Sparse Matrices
• A Bisection Method for Measuring the Distance of a Stable Matrix to the Unstable Matrices
• ARPACK Users' Guide
• Robust stability and a criss-cross algorithm for pseudospectra
• Deflation Techniques for an Implicitly Restarted Arnoldi Iteration
• On the computation of the real Hurwitz-stability radius
• Low-Rank Dynamics for Computing Extremal Points of Real Pseudospectra

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