Structured pseudospectra for polynomial eigenvalue problems, with applications. (English) Zbl 0996.65042

Tisseur, Françoise; Higham, Nicholas J.

SIAM J. Matrix Anal. Appl. 23, No. 1, 187-208 (2001).

This paper deals with the structured pseudospectra for polynomial eigenvalue problems. The connections between structured pseudospectra, structured backward errors and structured stability radii are investigated. Two approaches for computing pseudospectra are described. One is for general polynomial eigenvalue problem, the other is specific to quadratic eigenvalue problem. Several interesting examples from vibrating systems, control theory, and fluid mechanics are given to illustrate the techniques.

Reviewer: Liu Xinguo (Qingdao)

MSC:

65F15	Numerical computation of eigenvalues and eigenvectors of matrices
15A22	Matrix pencils

Keywords:

polynomial eigenvalue problem; \(\lambda\)-matrix; matrix polynomial; pseudospectrum; stability radius; backward error; transfer function; quadratic matrix equation; solvent; structured perturbations; Orr-Sommerfeld equation; numerical examples; quadratic eigenvalue problem

Software:

eigs; mctoolbox; Eigtool; ARPACK