A note on computation of pseudospectra

The aim is to contribute to pseudospectra computation via a path following technique. Given a matrix $A\in {‐C}^{n\times n}$ , we compute the branch consisting of a fixed singular value σ 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 s min((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.