Geodesic
Inverse spectral problem for an antisymmetric tridiagonal matrix
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 1026-1036.

Voir la notice de l'article provenant de la source Math-Net.Ru

The problem of recovering an antisymmetric tridiagonal matrix from the eigenvalues of this matrix and the normalizing constants for its eigenvectors is solved. Matrices of this type arise in the theory of small oscillations of mechanical systems and are related to the matrices of the systems through the Schrödinger transformation. The problem is solved by the method of orthogonal polynomials.
Keywords: inverse spectral problem, antisymmetric tridiagonal matrix, Schrödinger variables. 
@article{SEMR_2023_20_2_a64,
     author = {A. I. Gudimenko},
     title = {Inverse spectral problem for an antisymmetric tridiagonal matrix},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1026--1036},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a64/}
}
TY  - JOUR
AU  - A. I. Gudimenko
TI  - Inverse spectral problem for an antisymmetric tridiagonal matrix
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2023
SP  - 1026
EP  - 1036
VL  - 20
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a64/
LA  - ru
ID  - SEMR_2023_20_2_a64
ER  - 
%0 Journal Article
%A A. I. Gudimenko
%T Inverse spectral problem for an antisymmetric tridiagonal matrix
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2023
%P 1026-1036
%V 20
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a64/
%G ru
%F SEMR_2023_20_2_a64
A. I. Gudimenko. Inverse spectral problem for an antisymmetric tridiagonal matrix. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 1026-1036. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a64/

[1] G.M.L. Gladwell, “Matrix inverse eigenvalue problems”, Dynamical inverse problems. Theory and application, CISM Courses and Lectures, 529, eds. Gladwell Graham M. L. et al., Springer, Wien, 2011 | MR | Zbl

[2] G.M.L. Gladwell, Inverse problems in vibration, Solid Mechanics and its Applications, 119, Kluwer Academic Publishers, Dordrecht, 2004 | MR | Zbl

[3] M.T. Chu, G.H. Golub, Inverse eigenvalue problems: theory, algorithms, and applications, Oxford University Press, Oxford, 2005 | MR | Zbl

[4] F.R. Gantmacher, M.G. Krein, Oscillation matrices and kernels and small vibrations of mechanical systems, AMS Chelsea Publishing, Providence, 2002 | MR | Zbl

[5] E. Schrödinger, “Zur Dynamik gekoppelter Punktsysteme”, Ann. d. Physik (4), 44 (1914), 916–934 | DOI | Zbl

[6] M. Möller, V. Pivovarchik, Direct and inverse finite-dimensional spectral problems on graphs, Operator Theory: Advances and Applications, 283, Birkhäuser, Cham, 2020 | DOI | MR | Zbl

[7] Z.-W. Sun, “Generalized inverse eigenvalue problems for augmented periodic Jacobi matrices”, Comput. Appl. Math., 38:3 (2019), 104 | DOI | MR | Zbl

[8] M. Heydari, S.A. Shahzadeh Fazeli, S.M. Karbassi, M.R. Hooshmandasl, “On the inverse eigenvalue problem for periodic Jacobi matrices”, Inverse Probl. Sci. Eng., 28:9 (2020), 1253–1264 | DOI | MR | Zbl

[9] A.C. Mikhaylov, V.C. Mikhaylov, “Inverse problem for dynamical system associated with Jacobi matrices and classical moment problems”, J. Math. Anal. Appl., 487:1 (2020), 123970 | DOI | MR | Zbl

[10] A.C. Mikhaylov, V.C. Mikhaylov, “Inverse problems for finite Jacobi matrices and Krein-Stieltjes strings”, J. Inverse Ill-Posed Probl., 29:4 (2021), 611–628 | DOI | MR | Zbl

[11] W.-R. Xu, N. Bebiano, G.-L. Chen, “An inverse eigenvalue problem for modified pseudo-Jacobi matrices”, J. Comput. Appl. Math., 389 (2021), 113361 | DOI | MR | Zbl

[12] F.V. Atkinson, Discrete and continuous boundary problems, Mathematics in Science and Engineering, 8, Academic Press, New York-London, 1964 | MR | Zbl

[13] G.Sh. Guseinov, “On an inverse problem for two spectra of finite Jacobi matrices”, Appl. Math. Comput., 218:14 (2012), 7573–7589 | MR | Zbl

[14] N.I. Akhiezer, The classical moment problem and some related questions in analysis, Oliver Boyd, Edinburgh-London, 1965 | MR | Zbl

[15] F.R. Gantmacher, The theory of matrices, v. 1, AMS Chelsea Publishing, Providence, 1998 | MR | Zbl