A note on computation of pseudospectra

The aim is to contribute to pseudospectra computation via a path following technique. Given a matrix A∈ℂn×n, we compute the branch consisting of a fixed singular value ϵ and corresponding left and right singular vectors of the parameter dependent matrix (x+iy)I−A. The fact that the branch corresponds to the smallest singular value σmin((x+iy)I−A)=ϵ is sufficient to verify at just one point of the branch due to the continuity argument. We can exploit a standard ready-made software.