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We investigate recovery of the (Schr\"odinger) potential function from manyboundary measurements at a large wavenumber. By considering such a linearizedform, we obtain a H\"older type stability which is a big improvement over alogarithmic stability in low wavenumbers. Furthermore we extend the discussionto the linearized inverse Schr\"odinger potential problem with attenuation,where an exponential dependence of the attenuation constant is traced in thestability estimate. Based on the linearized problem, a reconstruction algorithmis proposed aiming at the recovery of the Fourier modes of the potentialfunction. By choosing the large wavenumber appropriately, we verify theefficiency of the proposed algorithm by several numerical examples.

Linearized inverse Schr\"odinger potential problem at a large wavenumber