On the complexity of the inverse Sturm-Liouville problem

Ben-Artzi, Jonathan ORCID: https://orcid.org/0000-0001-6184-9313, Marletta, Marco ORCID: https://orcid.org/0000-0003-1546-4046 and Rosler, Frank 2023. On the complexity of the inverse Sturm-Liouville problem. Pure and Applied Analysis 5 (4) , pp. 895-925. 10.2140/paa.2023.5.895

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Abstract

This paper explores the complexity associated with solving the inverse Sturm- Liouville problem with Robin boundary conditions: given a sequence of eigenvalues and a se- quence of norming constants, how many limits does a universal algorithm require to return the potential and boundary conditions? It is shown that if all but finitely many of the eigenvalues and norming constants coincide with those for the zero potential then the number of limits is zero, i.e. it is possible to retrieve the potential and boundary conditions precisely in finitely many steps. Otherwise, it is shown that this problem requires a single limit; moreover, if one has a priori control over how much the eigenvalues and norming constants differ from those of the zero-potential problem, and one knows that the average of the potential is zero, then the computation can be performed with complete error control. This is done in the spirit of the Solvability Complexity Index. All algorithms are provided explicitly along with numerical examples.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Publisher:	Mathematical Sciences Publishers
ISSN:	2578-5893
Date of First Compliant Deposit:	6 December 2023
Date of Acceptance:	26 May 2023
Last Modified:	13 Nov 2024 03:45
URI:	https://orca.cardiff.ac.uk/id/eprint/164545

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