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Inverse Iteration for Purely Imaginary Eigenvalues with Application to the Detection of Hopf Bifurcations in Large-Scale Problems

https://doi.org/10.1137/080742890
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Outgoing claims: the papers this work cites, builds on, or argues with.

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Elements of Applied Bifurcation Theory
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Two Methods for the Numerical Detection of Hopf Bifurcations
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A Parameter Free ADI-Like Method for the Numerical Solution of Large Scale Lyapunov Equations
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Shift-invert and Cayley transforms for detection of rightmost eigenvalues of nonsymmetric matrices
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Convergence of inexact inverse iteration with application to preconditioned iterative solves
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Complex shift and invert strategies for real matrices
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Numerical solution of the Lyapunov equation by approximate power iteration
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Eigenvalue decay bounds for solutions of Lyapunov equations: the symmetric case
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Inexact Inverse Iteration for Generalized Eigenvalue Problems
inferredcites →https://doi.org/10.1093/imanum/16.3.297openalex-snapshot
Matrix transformations for computing rightmost eigenvalues of large sparse non-symmetric eigenvalue problems
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Numerical Solution of the Stable, Non-negative Definite Lyapunov Equation Lyapunov Equation
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Mapping the dynamics of a bursting neuron
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Approximate solution of large sparse Lyapunov equations
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Fast Methods for Estimating the Distance to Uncontrollability
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A New Iterative Method for Solving Large-Scale Lyapunov Matrix Equations
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Convergence Analysis of Projection Methods for the Numerical Solution of Large Lyapunov Equations
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Krylov Subspace Methods for Solving Large Lyapunov Equations
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Stability and Stabilization of Time-Delay Systems: An Eigenvalue-Based Approach
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inferredcites →https://doi.org/10.1137/s0036142993253461openalex-snapshot
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inferredcites →https://doi.org/10.1137/s1064827596300073openalex-snapshot
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inferredcites →https://doi.org/10.1145/361573.361582openalex-snapshot
Algorithm 432 [C2]: Solution of the matrix equation AX + XB = C [F4]
inferredcites →https://doi.org/10.1201/b10511openalex-snapshot
Multiparameter Eigenvalue Problems
inferredcites →https://doi.org/10.24355/dbbs.084-200901220100-8openalex-snapshot
The spectrum of delay-differential equations: numerical methods, stability and perturbation
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What points at this work

Incoming claims: where this work appears in other papers’ reference lists and arguments.

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A Jacobi–Davidson method for two‐real‐parameter nonlinear eigenvalue problems arising from delay‐differential equations
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A Sylvester–Arnoldi type method for the generalized eigenvalue problem with two‐by‐two operator determinants
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Subspace methods for three‐parameter eigenvalue problems
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IFISS: A Computational Laboratory for Investigating Incompressible Flow Problems
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Lyapunov Inverse Iteration for Computing a Few Rightmost Eigenvalues of Large Generalized Eigenvalue Problems
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Computational Methods for Linear Matrix Equations
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New Algorithms for Computing the Real Structured Pseudospectral Abscissa and the Real Stability Radius of Large and Sparse Matrices
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Robust Linear Stability Analysis and a New Method for Computing the Action of the Matrix Exponential
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Preconditioned Low-Rank Methods for High-Dimensional Elliptic PDE Eigenvalue Problems
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Multiparameter Solution Methods for Semistructured Aeroelastic Flutter Problems
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Lyapunov Inverse Iteration for Stability Analysis using Computational Fluid Dynamics
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Low-rank tensor methods for linear systems and eigenvalue problems
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