In this note, given a matrix A∈Cn×n (or general polynomial P(z), z∈C) and an arbitrary scalar λ0∈C, we show how to define sequence μkk∈N which converges some element of its spectrum. The λ0 serves as initial term (μ0=λ0), while additional terms are constructed through recursive procedure, exploiting the fact that each μk is in point lying on boundary curve pseudospectral set A P(z)). Then, next...

where A1, . . . , Am are given n × n matrices and the functions p1, . . . , pm are assumed to be entire. This does not only include polynomial eigenvalue problems but also eigenvalue problems arising from systems of delay differential equations. Our aim is to compute the -pseudospectral abscissa, i.e. the real part of the rightmost point in the -pseudospectrum, which is the complex set obtained...