SIAM Journal on Applied Mathematics, Volume 80, Issue 1, Page 338-358, January 2020.
We investigate recovery of the (Schrödinger) potential function from many boundary measurements at a large wavenumber. By considering such a linearized form, we obtain a Hölder type stability which is a big improvement over a logarithmic stability in low wavenumbers. Furthermore we extend the discussion to the linearized inverse Schrödinger potential problem with attenuation, where an exponential dependence of the attenuation constant is traced in the stability estimate. Based on the linearized problem, a reconstruction algorithm is proposed aiming at the recovery of the Fourier modes of the potential function. By choosing the large wavenumber appropriately, we verify the efficiency of the proposed algorithm by several numerical examples.

中文翻译：

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大波数线性化薛定Sch逆势问题

SIAM应用数学杂志，第80卷，第1期，第338-358页，2020年1月。
我们从大波数下的许多边界测量中研究了（薛定ding ）势函数的恢复。通过考虑这种线性化形式，我们获得了Hölder型稳定性，这是对低波数对数稳定性的重大改进。此外，我们将讨论扩展到带衰减的线性Schrödinger逆电势问题，其中在稳定性估计中跟踪了衰减常数的指数相关性。在线性化问题的基础上，针对潜在函数的傅立叶模式的恢复，提出了一种重构算法。通过适当地选择了大波数，我们几个数值例子验证了算法的效率。