Structured pseudospectra for polynomial eigenvalue problems, with applications

SIAM Journal on Matrix Analysis and Applications

Volumn 23, Issue 1, 2002, Pages 187-208

  Tisseur, Françoise ^a   Higham, Nicholas J ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

matrix; Backward error; Matrix polynomial; Orr Sommerfeld equation; Polynomial eigenvalue problem; Pseudospectrum; Quadratic matrix equation; Solvent; Stability radius; Structured perturbations; Transfer function

Indexed keywords

EID: 0036058371     PISSN: 08954798     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895479800371451     Document Type: Article

References (52)

1. Differential eigenvalue problems in which the parameter appears nonlinearly
2. A note on the normwise perturbation theory for the regular generalized eigenproblem
3. Structured backward error and condition of generalized eigenvalue problems
4. Solving a quadratic matrix equation by Newton's method with exact line searches
5. Numerical analysis of a quadratic matrix equation
6. A block algorithm for matrix 1-norm estimation, with an application to 1-norm pseudospectra
7. Bounds for eigenvalues of matrix polynomials
8. More on pseudospectra for polynomial eigenvalue problems and applications in control theory
9. Spectral value sets: A graphical tool for robustness analysis
10. Real and complex stability radii: A survey
11. Numerical solution of matrix polynomial equations by Newton's method
12. Efficient multivariable frequency response computations
13. Numerical range of matrix polynomials
14. Computation of pseudospectra by continuation
15. Locking and restarting quadratic eigenvalue solvers
16. A determinant identity and its application in evaluating frequency response matrices
17. Root neighborhoods of a polynomial
18. Accurate solution of the Orr-Sommerfeld stability equation
19. Robust stability of linear systems described by higher order dynamic equations
20. Pseudospeetra of the Orr-Sommerfeld operator
21. Generalized epsilon-pseudospeetra
22. Transfer functions and resolvent norm approximation of large matrices
23. Jacobi-Davidson type methods for generalized eigenproblems and polynomial eigenproblems
24. Backward error and condition of polynomial eigenvalue problems
25. The quadratic eigenvalue problem
26. Pseudozeros of polynomials and pseudospectra of companion matrices
27. Calculation of pseudospectra by the Arnoldi iteration
28. Pseudospectra of matrices
29. Computation of pseudospectra
30. Spectra and pseudospectra
31. Hydrodynamic stability without eigenvalues
32. On stability radii of generalized eigenvalue problems
33. Pseudospeetra for matrix pencils and stability of equilibria