This is an anharmonic oscillator, -u_xx + cx2u, for c=1+3i, discretised using a Chebyshev spectral method [3]. Since this discretization includes numerous spurious eigenvalues, the matrix is projected onto an appropriate invariant subspace to accelerate computation of the pseudospectra. This example was first studied by Brian Davies [1,2].
[1]: E. B. Davies, "Pseudo-spectra, the harmonic oscillator and complex resonances", Proc. Roy. Soc. Lond. Ser. A 455 (1999), pp. 585-599.
[2]: E. B. Davies, "Semi-classical states for non-self-adjoint Schroedinger operators", Commun. Math. Phys. 200 (1999), pp. 35-41.
[3]: L. N. Trefethen, "Spectral methods in MATLAB", SIAM, 2000.
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