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Inverse Problems in Science and Engineering Volume 27, 2019 - Issue 6
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Original Articles

Generalized inverse spectral problem for pseudo-Jacobi matrices with mixed eigendata

Wei-Ru XuSchool of Mathematical Sciences, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai, People's Republic of China;CMUC, Department of Mathematics, University of Coimbra, Coimbra, PortugalCorrespondence[email protected]
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,
Natália BebianoCMUC, Department of Mathematics, University of Coimbra, Coimbra, PortugalView further author information
&
Guo-Liang ChenSchool of Mathematical Sciences, Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice, East China Normal University, Shanghai, People's Republic of ChinaView further author information
Pages 773-789 | Received 04 Dec 2017, Accepted 28 Jun 2018, Published online: 18 Jul 2018

References

  • Bebiano N, da Providência J. Inverse problems for pseudo-Jacobi matrices: existence and uniqueness results. Inverse Prob. 2011;27:025005. (12 p.). doi: 10.1088/0266-5611/27/2/025005
  • Akhiezer NI. The classical moment problem. New York: Hafner; 1965. (Engl. Transl.).
  • Bebiano N, da Providência J. Corrigendum: inverse problems for pseudo-Jacobi matrices: existence and uniqueness results. Inverse Prob. 2012;28:069501. (1 p.). doi: 10.1088/0266-5611/28/6/069501
  • da Providência J, Bebiano N, da Providência JP. Non-Hermitian Hamiltonians with real spectrum in quantum mechanics. Braz J Phys. 2011;41:78–85. doi: 10.1007/s13538-011-0010-9
  • Hochstadt H. On the construction of a Jacobi matrix from spectral data. Linear Algebra Appl. 1974;8:435–446. doi: 10.1016/0024-3795(74)90077-9
  • Hald OH. Inverse eigenvalue problems for Jacobi matrices. Linear Algebra Appl. 1976;14:63–85. doi: 10.1016/0024-3795(76)90064-1
  • Boley D, Golub GH. A survey of matrix inverse eigenvalue problem. Inverse Prob. 1987;3:595–622. doi: 10.1088/0266-5611/3/4/010
  • Ferguson WE. The construction of Jacobi and periodic Jacobi matrices with prescribed spectra. Math Comp. 1980;35:1203–1220. doi: 10.1090/S0025-5718-1980-0583498-3
  • Borges CF, Frezza R, Gragg WB. Some inverse eigenproblems for Jacobi and arrow matrices. Numer Linear Algebra Appl. 1995;2:195–203. doi: 10.1002/nla.1680020302
  • Chu MT, Golub GH. Inverse eigenvalue problems: theory, algorithms, and application. New York: Oxford Science Publications, Oxford University Press; 2005.
  • Cox SJ, Embree M, Hokanson JM. One can hear the composition of a string: experiments with an inverse eigenvalue problem. SIAM Rev. 2012;54:157–178. doi: 10.1137/080731037
  • Gladwell GML. Inverse problems in vibration. Dordrecht: Kluwer Academic Publishers; 2004.
  • Peng Z-Y, Hu X-Y, Zhang L. On the construction of a Jacobi matrix from its mixed-type eigenpairs. Linear Algebra Appl. 2003;362:191–200. doi: 10.1016/S0024-3795(02)00488-3
  • Xu S-F. On the Jacobi matrix inverse eigenvalue problem with mixed given data. SIAM J Matrix Anal Appl. 1996;17:632–639. doi: 10.1137/S089547989122065X
  • Xu W-R, Chen G-L. On inverse eigenvalue problems for two kinds of special banded matrices. Filomat. 2017;31(2):371–385. doi: 10.2298/FIL1702371X
  • Bebiano N, Furtado S, da Providência J. An algorithm for constructing a pseudo-Jacobi matrix from given spectral data. Numer Linear Algebra Appl. 2013;20:185–197. doi: 10.1002/nla.1855
  • Xu W-R, Bebiano N, Chen G-L. An inverse eigenvalue problem for pseudo-Jacobi matrices. Appl Math Comput. Submitted for publication 2017.
  • Ghanbari K, Parvizpour F. Generalized inverse eigenvalue problem with mixed eigendata. Linear Algebra Appl. 2012;437:2056–2063. doi: 10.1016/j.laa.2012.05.020
  • Sen M, Sharma D. Generalized inverse eigenvalue problem for matrices whose graph is a path. Linear Algebra Appl. 2014;446:224–236. doi: 10.1016/j.laa.2013.12.035

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