Inverse Sturm-Liouville problems: some recent developments

Alan Andrew

Abstract


We consider numerical methods for obtaining, from spectral data, information on the potentials of Sturm--Liouville operators. In particular, we describe some recent work on methods using an asymptotic correction technique of Paine, de Hoog and Anderssen. Topics covered include a discussion of difficulties arising from the scarcity of accurate data in physical applications, a preview of some work in progress on the Hochstadt--Lieberman problem, and suggestions for future work.

References

Keywords


inverse Sturm-Liouville problems, asymptotic correction, eigenvalues

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DOI: http://dx.doi.org/10.21914/anziamj.v52i0.3888



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.