Standard perturbation theory of eigenvalue problems consists of obtaining approximations of eigenmodes in the neighborhood of a Hamiltonian where the corresponding eigenmode is known. Nevertheless, if the corresponding eigenmodes of several nearby Hamiltonians are known, standard perturbation theory cannot simultaneously use all this knowledge to provide a better approximation. We derive a formula enabling such an approximation result, and provide numerical examples for which this method is more competitive than standard perturbation theory.

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