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.References
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Additional Information
- Xinfu Chen
- Affiliation: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260
- MR Author ID: 261335
- Email: xinfu@pitt.edu
- Y. H. Cheng
- Affiliation: Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan
- Email: jengyh@math.nsysu.edu.tw
- C. K. Law
- Affiliation: Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan – and – National Center for Theoretical Sciences, Taiwan
- Email: law@math.nsysu.edu.tw
- Received by editor(s): November 4, 2008
- Received by editor(s) in revised form: November 18, 2009
- Published electronically: April 20, 2011
- © Copyright 2011 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 363 (2011), 4831-4851
- MSC (2010): Primary 34B24, 47A52; Secondary 34A55, 49M30
- DOI: https://doi.org/10.1090/S0002-9947-2011-05258-X
- MathSciNet review: 2806693