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