Inverse eigenvalue problem for constructing a kind of acyclic matrices with two eigenpairs

Maryam Babaei Zarch; Seyed Abolfazl Shahzadeh Fazeli; Seyed Mehdi Karbassi

Applications of Mathematics (2020)

  • Volume: 65, Issue: 1, page 89-103
  • ISSN: 0862-7940

Abstract

top
We investigate an inverse eigenvalue problem for constructing a special kind of acyclic matrices. The problem involves the reconstruction of the matrices whose graph is an m -centipede. This is done by using the ( 2 m - 1 ) st and ( 2 m ) th eigenpairs of their leading principal submatrices. To solve this problem, the recurrence relations between leading principal submatrices are used.

How to cite

top

Babaei Zarch, Maryam, Shahzadeh Fazeli, Seyed Abolfazl, and Karbassi, Seyed Mehdi. "Inverse eigenvalue problem for constructing a kind of acyclic matrices with two eigenpairs." Applications of Mathematics 65.1 (2020): 89-103. <http://eudml.org/doc/295017>.

@article{BabaeiZarch2020,
abstract = {We investigate an inverse eigenvalue problem for constructing a special kind of acyclic matrices. The problem involves the reconstruction of the matrices whose graph is an $m$-centipede. This is done by using the $(2m-1)$st and $(2m)$th eigenpairs of their leading principal submatrices. To solve this problem, the recurrence relations between leading principal submatrices are used.},
author = {Babaei Zarch, Maryam, Shahzadeh Fazeli, Seyed Abolfazl, Karbassi, Seyed Mehdi},
journal = {Applications of Mathematics},
keywords = {inverse eigenvalue problem; leading principal submatrices; graph of a matrix; eigenpair},
language = {eng},
number = {1},
pages = {89-103},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Inverse eigenvalue problem for constructing a kind of acyclic matrices with two eigenpairs},
url = {http://eudml.org/doc/295017},
volume = {65},
year = {2020},
}

TY - JOUR
AU - Babaei Zarch, Maryam
AU - Shahzadeh Fazeli, Seyed Abolfazl
AU - Karbassi, Seyed Mehdi
TI - Inverse eigenvalue problem for constructing a kind of acyclic matrices with two eigenpairs
JO - Applications of Mathematics
PY - 2020
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 1
SP - 89
EP - 103
AB - We investigate an inverse eigenvalue problem for constructing a special kind of acyclic matrices. The problem involves the reconstruction of the matrices whose graph is an $m$-centipede. This is done by using the $(2m-1)$st and $(2m)$th eigenpairs of their leading principal submatrices. To solve this problem, the recurrence relations between leading principal submatrices are used.
LA - eng
KW - inverse eigenvalue problem; leading principal submatrices; graph of a matrix; eigenpair
UR - http://eudml.org/doc/295017
ER -

References

top
  1. Andrade, E., Gomes, H., Robbiano, M., Spectra and Randić spectra of caterpillar graphs and applications to the energy, MATCH Commun. Math. Comput. Chem. 77 (2017), 61-75. (2017) MR3645367
  2. Bu, C., Zhou, J., Li, H., 10.2298/FIL1206123B, Filomat 26 (2012), 1123-1131. (2012) Zbl1289.05271MR3099573DOI10.2298/FIL1206123B
  3. 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
  4. Duarte, A. L., 10.1016/0024-3795(89)90295-4, Linear Algebra Appl. 113 (1989), 173-182. (1989) Zbl0661.15024MR0978591DOI10.1016/0024-3795(89)90295-4
  5. Elhay, S., Gladwell, G. M. L., Golub, G. H., Ram, Y. M., 10.1137/S089547989631072X, SIAM J. Matrix Anal. Appl. 20 (1999), 563-574. (1999) Zbl0929.15008MR1685042DOI10.1137/S089547989631072X
  6. Ghanbari, K., Parvizpour, F., 10.1016/j.laa.2012.05.020, Linear Algebra Appl. 437 (2012), 2056-2063. (2012) Zbl1262.15017MR2950471DOI10.1016/j.laa.2012.05.020
  7. Hogben, L., 10.13001/1081-3810.1174, Electron. J. Linear Algebra 14 (2005), 12-31. (2005) Zbl1162.05333MR2202430DOI10.13001/1081-3810.1174
  8. 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
  9. Nair, R., Shader, B. L., 10.1016/j.laa.2012.08.029, Linear Algebra Appl. 438 (2013), 4075-4089. (2013) Zbl1282.05142MR3034516DOI10.1016/j.laa.2012.08.029
  10. 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
  11. 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
  12. Pickmann, H., Egaña, J., Soto, R. L., 10.1016/j.laa.2007.07.020, Linear Algebra Appl. 427 (2007), 256-271. (2007) Zbl1144.65026MR2351358DOI10.1016/j.laa.2007.07.020
  13. Pivovarchik, V., Rozhenko, N., Tretter, C., 10.1016/j.laa.2013.07.003, Linear Algebra Appl. 439 (2013), 2263-2292. (2013) Zbl1286.34025MR3091304DOI10.1016/j.laa.2013.07.003
  14. Sen, M., Sharma, D., 10.1016/j.laa.2013.12.035, Linear Algebra Appl. 446 (2014), 224-236. (2014) Zbl1286.65050MR3163141DOI10.1016/j.laa.2013.12.035
  15. Sharma, D., Sen, M., 10.3390/math4010012, Mathematics 4 (2016), Article ID 12, 11 pages. (2016) Zbl1382.65109DOI10.3390/math4010012
  16. Sharma, D., Sen, M., 10.1515/spma-2018-0008, Spec. Matrices 6 (2018), 77-92. (2018) Zbl1391.15098MR3764333DOI10.1515/spma-2018-0008
  17. Zhang, Y., On the general algebraic inverse eigenvalue problems, J. Comput. Math. 22 (2004), 567-580. (2004) Zbl1066.65044MR2072173

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.