Pseudospectrum Enclosures by Discretization

Abstract A new method to enclose the pseudospectrum via numerical range of inverse a matrix or linear operator is presented. The applied finite-dimensional discretizations an on infinite-dimensional Hilbert space, and convergence results for different approximation schemes are obtained, including finite element methods. We show that full contained in intersection sets which expressed terms ranges shifted inverses approximating matrices. illustrated by means two examples: advection–diffusion Hain–Lüst operator.