Computing unstructured and structured polynomial pseudospectrum approximations
In many applications it is important to sensitivity of eigenvalues of a matrix polynomial polynomial. The sensitivity commonly is described pseudospectra. However, the determination of pseudospectra of matrix polynomials is very demanding computationally. This paper describes a new approach to computing approximations of pseudospectra of matrix polynomials by using rank-one or projected rank-one perturbations. These perturbations are inspired by Wilkinson's analysis of eigenvalue sensitivity. This approach allows the approximation of both structured and unstructured pseudospectra.