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Recovering boundary conditions in inverse Sturm-Liouville problems

Norbert Roehrl
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Abstract

We introduce a variational algorithm, which solves the classical inverse Sturm-Liouville problem when two spectra are given. In contrast to other approaches, it recovers the potential as well as the boundary conditions without a priori knowledge of the mean of the potential. Numerical examples show that the algorithm works quite reliable, even in the presence of noise. A proof of the absence of strict local minimizers of the functional supports the observation, that a good initial guess is not essential.

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Norbert Roehrl. 2006-01-02. Recovering boundary conditions in inverse Sturm-Liouville problems. https://arxiv.org/abs/math/0601031

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