Abstract: The projection methods, usually viewed as the methods
for computing eigenvalues, can also be used to estimate pseudospectra.
This paper proposes a kind of projection methods for computing
the pseudospectra of large scale matrices, including orthogonalization
projection method and oblique projection method respectively. This
possibility may be of practical importance in applications involving
large scale highly nonnormal matrices. Numerical algorithms are
given and some numerical experiments illustrate the efficiency of
the new algorithms.