A note on structured pseudospectra
Journal of Computational and Applied Mathematics
Pseudospectra and delay differential equations
Journal of Computational and Applied Mathematics
Note on structured indefinite perturbations to Hermitian matrices
Journal of Computational and Applied Mathematics
Structured pseudospectra and structured sensitivity of eigenvalues
Journal of Computational and Applied Mathematics
Computing the topology of a real algebraic plane curve whose equation is not directly available
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Geometric applications of the Bezout matrix in the Lagrange basis
Proceedings of the 2007 international workshop on Symbolic-numeric computation
Structured pseudospectra for nonlinear eigenvalue problems
Journal of Computational and Applied Mathematics
Pseudospectra for exponential polynomial matrices
Proceedings of the 2009 conference on Symbolic numeric computation
A note on structured pseudospectra
Journal of Computational and Applied Mathematics
Partial eigenvalue assignment problem of high order control systems using orthogonality relations
Computers & Mathematics with Applications
SIAM Journal on Matrix Analysis and Applications
On Pseudospectra, Critical Points, and Multiple Eigenvalues of Matrix Pencils
SIAM Journal on Matrix Analysis and Applications
An improved grid method for the computation of the pseudospectra of matrix polynomials
Mathematical and Computer Modelling: An International Journal
NLEVP: A Collection of Nonlinear Eigenvalue Problems
ACM Transactions on Mathematical Software (TOMS)
Pseudospectra of exponential matrix polynomials
Theoretical Computer Science
Implementation of Pellet's theorem
Numerical Algorithms
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Pseudospectra associated with the standard and generalized eigenvalue problems have been widely investigated in recent years. We extend the usual definitions in two respects, by treating the polynomial eigenvalue problem and by allowing structured perturbations of a type arising in control theory. We explore connections between structured pseudospectra, structured backward errors, and structured stability radii. Two main approaches for computing pseudospectra are described. One is based on a transfer function and employs a generalized Schur decomposition of the companion form pencil. The other, specific to quadratic polynomials, finds a solvent of the associated quadratic matrix equation and thereby factorizes the quadratic $\lambda$-matrix. Possible approaches for large, sparse problems are also outlined. A collection of examples from vibrating systems, control theory, acoustics, and fluid mechanics is given to illustrate the techniques.