Inverse problems for Jacobi operators. I: Interior mass-spring perturbations in finite systems (Q2888755)
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scientific article; zbMATH DE number 6042578
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inverse problems for Jacobi operators. I: Interior mass-spring perturbations in finite systems |
scientific article; zbMATH DE number 6042578 |
Statements
4 June 2012
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Jacobi matrix
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inverse problem
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perturbation
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0.98443687
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0.9732183
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0.97303426
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0.8908316
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0.8813085
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0.8781315
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0.8778639
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Inverse problems for Jacobi operators. I: Interior mass-spring perturbations in finite systems (English)
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The paper deals with the problem of the reconstruction of a finite Jacobi matrix by its spectrum, and the spectrum of its 3-rank perturbation of a special type. The question is generated by the problem of finding characteristics of a system of point masses and connective springs by its frequencies, and the frequencies of a perturbed system with an interior mass changed and a new spring attached to this mass. The authors find a constructive algorithm for the recovery of the matrix by two spectra and an additional parameter. They give necessary and sufficient conditions on the spectral data and solve completely the corresponding inverse problem.
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