On an inverse problem for two spectra of finite Jacobi matrices

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Date

2012

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Elsevier Science inc

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Mathematics
(2000)
The Atılım University Department of Mathematics was founded in 2000 and it offers education in English. The Department offers students the opportunity to obtain a certificate in Mathematical Finance or Cryptography, aside from their undergraduate diploma. Our students may obtain a diploma secondary to their diploma in Mathematics with the Double-Major Program; as well as a certificate in their minor alongside their diploma in Mathematics through the Minor Program. Our graduates may pursue a career in academics at universities, as well as be hired in sectors such as finance, education, banking, and informatics. Our Department has been accredited by the evaluation and accreditation organization FEDEK for a duration of 5 years (until September 30th, 2025), the maximum FEDEK accreditation period achievable. Our Department is globally and nationally among the leading Mathematics departments with a program that suits international standards and a qualified academic staff; even more so for the last five years with our rankings in the field rankings of URAP, THE, USNEWS and WEBOFMETRIC.

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Abstract

We solve a version of the inverse spectral problem for two spectra of finite order real Jacobi matrices. The problem is to reconstruct the matrix using two sets of eigenvalues, one for the original Jacobi matrix and one for the matrix obtained by replacing the last diagonal element of the Jacobi matrix by some another number. The uniqueness and existence results for solution of the inverse problem are established and an explicit procedure of reconstruction of the matrix from the two spectra is given. (C) 2012 Elsevier Inc. All rights reserved.

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Keywords

Jacobi matrix, Difference equation, Spectrum, Normalizing number, Inverse problem

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Citation

8

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Volume

218

Issue

14

Start Page

7573

End Page

7589

URI

https://doi.org/10.1016/j.amc.2012.01.024
 https://hdl.handle.net/20.500.14411/1369

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