On the inverse eigenvalue problem for a special kind of acyclic matrices

Mohammad Heydari; Seyed Abolfazl Shahzadeh Fazeli; Seyed Mehdi Karbassi

Applications of Mathematics (2019)

  • Volume: 64, Issue: 3, page 351-366
  • ISSN: 0862-7940

Abstract

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We study an inverse eigenvalue problem (IEP) of reconstructing a special kind of symmetric acyclic matrices whose graph is a generalized star graph. The problem involves the reconstruction of a matrix by the minimum and maximum eigenvalues of each of its leading principal submatrices. To solve the problem, we use the recurrence relation of characteristic polynomials among leading principal minors. The necessary and sufficient conditions for the solvability of the problem are derived. Finally, a numerical algorithm and some examples are given.

How to cite

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Heydari, Mohammad, Shahzadeh Fazeli, Seyed Abolfazl, and Karbassi, Seyed Mehdi. "On the inverse eigenvalue problem for a special kind of acyclic matrices." Applications of Mathematics 64.3 (2019): 351-366. <http://eudml.org/doc/294726>.

@article{Heydari2019,
abstract = {We study an inverse eigenvalue problem (IEP) of reconstructing a special kind of symmetric acyclic matrices whose graph is a generalized star graph. The problem involves the reconstruction of a matrix by the minimum and maximum eigenvalues of each of its leading principal submatrices. To solve the problem, we use the recurrence relation of characteristic polynomials among leading principal minors. The necessary and sufficient conditions for the solvability of the problem are derived. Finally, a numerical algorithm and some examples are given.},
author = {Heydari, Mohammad, Shahzadeh Fazeli, Seyed Abolfazl, Karbassi, Seyed Mehdi},
journal = {Applications of Mathematics},
keywords = {inverse eigenvalue problem; leading principal minor; graph of a matrix},
language = {eng},
number = {3},
pages = {351-366},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the inverse eigenvalue problem for a special kind of acyclic matrices},
url = {http://eudml.org/doc/294726},
volume = {64},
year = {2019},
}

TY - JOUR
AU - Heydari, Mohammad
AU - Shahzadeh Fazeli, Seyed Abolfazl
AU - Karbassi, Seyed Mehdi
TI - On the inverse eigenvalue problem for a special kind of acyclic matrices
JO - Applications of Mathematics
PY - 2019
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 3
SP - 351
EP - 366
AB - We study an inverse eigenvalue problem (IEP) of reconstructing a special kind of symmetric acyclic matrices whose graph is a generalized star graph. The problem involves the reconstruction of a matrix by the minimum and maximum eigenvalues of each of its leading principal submatrices. To solve the problem, we use the recurrence relation of characteristic polynomials among leading principal minors. The necessary and sufficient conditions for the solvability of the problem are derived. Finally, a numerical algorithm and some examples are given.
LA - eng
KW - inverse eigenvalue problem; leading principal minor; graph of a matrix
UR - http://eudml.org/doc/294726
ER -

References

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  1. Chu, M. T., Golub, G. H., 10.1093/acprof:oso/9780198566649.001.0001, Numerical Mathematics and Scientific Computation, Oxford University Press, Oxford (2005). (2005) Zbl1075.65058MR2263317DOI10.1093/acprof:oso/9780198566649.001.0001
  2. Coakley, E. S., Rokhlin, V., 10.1016/j.acha.2012.06.003, Appl. Comput. Harmon. Anal. 34 (2013), 379-414. (2013) Zbl1264.65051MR3027910DOI10.1016/j.acha.2012.06.003
  3. Hogben, L., 10.13001/1081-3810.1174, Electron. J. Linear Algebra 14 (2005), 12-31. (2005) Zbl1162.05333MR2202430DOI10.13001/1081-3810.1174
  4. Johnson, C. R., Duarte, A. L., Saiago, C. M., 10.1016/S0024-3795(03)00582-2, Linear Algebra Appl. 373 (2003), 311-330. (2003) Zbl1035.15010MR2022294DOI10.1016/S0024-3795(03)00582-2
  5. Monfared, K. H., Shader, B. L., 10.1016/j.laa.2013.01.036, Linear Algebra Appl. 438 (2013), 4348-4358. (2013) Zbl1282.05141MR3034535DOI10.1016/j.laa.2013.01.036
  6. Nylen, P., Uhlig, F., 10.1016/S0024-3795(96)00316-3, Linear Algebra Appl. 254 (1997), 409-425. (1997) Zbl0879.15007MR1436689DOI10.1016/S0024-3795(96)00316-3
  7. Peng, J., Hu, X.-Y., Zhang, L., 10.1016/j.laa.2005.11.017, Linear Algebra Appl. 416 (2006), 336-347. (2006) Zbl1097.65053MR2242733DOI10.1016/j.laa.2005.11.017
  8. Sharma, D., Sen, M., 10.3390/math4010012, Mathematics 4 (2016), Article ID 12, 11 pages. (2016) Zbl1382.65109DOI10.3390/math4010012
  9. Sharma, D., Sen, M., 10.1515/spma-2018-0008, Spec. Matrices 6 (2018), 77-92. (2018) Zbl1391.15098MR3764333DOI10.1515/spma-2018-0008
  10. Xu, W.-R., Chen, G.-L., 10.2298/FIL1702371X, Filomat 31 (2017), 371-385. (2017) MR3628846DOI10.2298/FIL1702371X

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