We present new residual estimates based on Kato’s square root theorem for spectral approximations of non-self-adjoint differential operators of convection–diffusion–reaction type. It is not assumed that the eigenvalue/vector approximations are obtained from any particular numerical method, so these estimates may be applied quite broadly. Key eigenvalue and eigenvector error results are illustrated in the context of an hp-adaptive finite element algorithm for spectral computations, where it is shown that the resulting a posteriori error estimates are reliable. The efficiency of these error estimates is also strongly suggested empirically.
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