SavedAdd your journal

Journals / Hacettepe Journal of Mathematics and Statistics / 2011 / Cilt: 40 - Sayı: 2

Construction of a complex Jacobi matrix from two-spectra

Gusein Sh. GUSEİNOV
Pages
297–303
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

An explicit procedure of reconstruction of the matrix from the two-spectra is given.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we study the inverse spectral problem for two-spectra of finite order complex Jacobi matrices (tri-diagonal matrices).
📊
Key Findings & Data:The prob- lem is to reconstruct the matrix using two sets of eigenvalues, one for the original Jacobi matrix and one for the matrix obtained by delet- ing the first column and the first row of the Jacobi matrix.
💡
Conclusion & Impact:An explicit procedure of reconstruction of the matrix from the two-spectra is given.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

In this paper we study the inverse spectral problem for two-spectra of finite order complex Jacobi matrices (tri-diagonal matrices). The prob- lem is to reconstruct the matrix using two sets of eigenvalues, one for the original Jacobi matrix and one for the matrix obtained by delet- ing the first column and the first row of the Jacobi matrix. An explicit procedure of reconstruction of the matrix from the two-spectra is given.

🔖

Cite This Article

GUSEİNOV, G. S. (2022). Construction of a complex Jacobi matrix from two-spectra. Hacettepe Journal of Mathematics and Statistics, Cilt: 40 - Sayı: 2, 297–303. https://ajindex.com/articles/530601

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (10)

  1. Chu, M.T. and Golub, G.H. Inverse Eigenvalue Problems: Theory, Algorithms, and Ap- plications (Oxford University Press, New York, 2005)
  2. Fu, L. and Hochstadt, H. Inverse theorems for Jacobi matrices, J. Math. Anal. Appl. 47, 162–168, 1974
  3. Gasymov, M.G. and Guseinov, G. Sh. On inverse problems of spectral analysis for infinite Jacobi matrices in the limit-circle case, Dokl. Akad. Nauk SSSR 309, 1293–1296, 1989; English transl. in Soviet Math. Dokl. 40, 627–630, 1990
  4. Gesztesy, F. and Simon, B.M. M-functions and inverse spectral analysis for finite and semi-infinite Jacobi matrices, J. Anal. Math. 73, 267–297, 1997
  5. Gray, L. J. and Wilson, D.G. Construction of a Jacobi matrix from spectral data, Linear Algebra Appl. 14, 131–134, 1976
  6. Guseinov, G. Sh. Determination of the infinite Jacobi matrix with respect to two-spectra, Mat. Zametki 23, 709–720, 1978; English transl. in Math. Notes 23, 391–398, 1978
  7. Guseinov, G. Sh. Inverse spectral problems for tridiagonal N by N complex Hamiltonians, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 5, Paper 018, 28 pages, 2009
  8. Hald, O.H. Inverse eigenvalue problems for Jacobi matrices, Linear Algebra Appl. 14, 63– 85, 1976
  9. Hochstadt, H. On some inverse problems in matrix theory, Arch. Math. 18, 201–207, 1967
  10. Hochstadt, H. On construction of a Jacobi matrix from spectral data, Linear Algebra Appl. 8, 435–446, 1974.