Reconstructing potentials from zeros of one eigenfunction

Chen, Xinfu; Cheng, Y.; Law, C.

doi:10.1090/S0002-9947-2011-05258-X

Reconstructing potentials from zeros of one eigenfunction
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by Xinfu Chen, Y. H. Cheng and C. K. Law PDF

Trans. Amer. Math. Soc. 363 (2011), 4831-4851 Request permission

Abstract:

We study an inverse nodal problem, concerning the reconstruction of a potential of a Sturm-Liouville operator, by using zeros of one eigenfunction as input. We propose three methods for the reconstruction, one of which is the Tikhonov regularization method. The explicit error bounds are calculated for all three methods. In case there is measurement error, the Tikhonov regularization method is still convergent. The study is motivated by physical considerations.

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