a note on computation of pseudospectra

the aim is to contribute to pseudospectra computation via a path following technique. given a matrix a∈c^n×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.