Numerical algorithms for inverse Sturm-Liouville problems

In this paper, two classical inverse spectral problems are investigated, namely, the inverse second-order Sturm-Liouville problem and the inverse fourth-order Sturm-Liouville problem. Based on Lidskii’s theorem, we derive trace formulas showing relations between the unknown coefficients and eigenval...

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Bibliographic Details
Published in:Numerical algorithms Vol. 89; no. 3; pp. 1287 - 1309
Main Authors: Jiang, Xiaoying, Li, Xiaowen, Xu, Xiang
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2022
Springer Nature B.V
Subjects:
Algebra
Algorithms
Boundary conditions
Computer Science
Eigenvalues
Lie groups
Numeric Computing
Numerical Analysis
Original Paper
Theory of Computation
Reconstruction algorithms
Trace formulas
Inverse spectral problems
ISSN:1017-1398, 1572-9265
Online Access:Get full text
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Summary:In this paper, two classical inverse spectral problems are investigated, namely, the inverse second-order Sturm-Liouville problem and the inverse fourth-order Sturm-Liouville problem. Based on Lidskii’s theorem, we derive trace formulas showing relations between the unknown coefficients and eigenvalues explicitly for both problems. According to those trace formulas, two efficient algorithms are proposed to recover the symmetric potential from one spectrum for second-order Sturm-Liouville problem and two coefficients simultaneously from three spectra for fourth-order Sturm-Liouville problem, respectively. Numerical results are presented to illustrate the effectiveness of the proposed reconstruction algorithms.
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-021-01153-2