| Title:
|
Inverse eigenvalue problem for constructing a kind of acyclic matrices with two eigenpairs (English) |
| Author:
|
Babaei Zarch, Maryam |
| Author:
|
Shahzadeh Fazeli, Seyed Abolfazl |
| Author:
|
Karbassi, Seyed Mehdi |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
65 |
| Issue:
|
1 |
| Year:
|
2020 |
| Pages:
|
89-103 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
inverse eigenvalue problem |
| Keyword:
|
leading principal submatrices |
| Keyword:
|
graph of a matrix |
| Keyword:
|
eigenpair |
| MSC:
|
05C50 |
| MSC:
|
65F18 |
| idZBL:
|
07177873 |
| idMR:
|
MR4064591 |
| DOI:
|
10.21136/AM.2020.0103-19 |
| . |
| Date available:
|
2020-02-20T09:46:59Z |
| Last updated:
|
2022-03-07 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147996 |
| . |
| Reference:
|
[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. MR 3645367 |
| Reference:
|
[2] Bu, C., Zhou, J., Li, H.: Spectral determination of some chemical graphs.Filomat 26 (2012), 1123-1131. Zbl 1289.05271, MR 3099573, 10.2298/FIL1206123B |
| Reference:
|
[3] Chu, M. T., Golub, G. H.: Inverse Eigenvalue Problems: Theory, Algorithms, and Applications.Numerical Mathematics and Scientific Computation, Oxford University Press, Oxford (2005). Zbl 1075.65058, MR 2263317, 10.1093/acprof:oso/9780198566649.001.0001 |
| Reference:
|
[4] Duarte, A. L.: Construction of acyclic matrices from spectral data.Linear Algebra Appl. 113 (1989), 173-182. Zbl 0661.15024, MR 0978591, 10.1016/0024-3795(89)90295-4 |
| Reference:
|
[5] Elhay, S., Gladwell, G. M. L., Golub, G. H., Ram, Y. M.: On some eigenvector-eigenvalue relations.SIAM J. Matrix Anal. Appl. 20 (1999), 563-574. Zbl 0929.15008, MR 1685042, 10.1137/S089547989631072X |
| Reference:
|
[6] Ghanbari, K., Parvizpour, F.: Generalized inverse eigenvalue problem with mixed eigendata.Linear Algebra Appl. 437 (2012), 2056-2063. Zbl 1262.15017, MR 2950471, 10.1016/j.laa.2012.05.020 |
| Reference:
|
[7] Hogben, L.: Spectral graph theory and the inverse eigenvalue problem of a graph.Electron. J. Linear Algebra 14 (2005), 12-31. Zbl 1162.05333, MR 2202430, 10.13001/1081-3810.1174 |
| Reference:
|
[8] Monfared, K. H., Shader, B. L.: Construction of matrices with a given graph and prescribed interlaced spectral data.Linear Algebra Appl. 438 (2013), 4348-4358. Zbl 1282.05141, MR 3034535, 10.1016/j.laa.2013.01.036 |
| Reference:
|
[9] Nair, R., Shader, B. L.: Acyclic matrices with a small number of distinct eigenvalues.Linear Algebra Appl. 438 (2013), 4075-4089. Zbl 1282.05142, MR 3034516, 10.1016/j.laa.2012.08.029 |
| Reference:
|
[10] Nylen, P., Uhlig, F.: Inverse eigenvalue problems associated with spring-mass systems.Linear Algebra Appl. 254 (1997), 409-425. Zbl 0879.15007, MR 1436689, 10.1016/S0024-3795(96)00316-3 |
| Reference:
|
[11] Peng, J., Hu, X.-Y., Zhang, L.: Two inverse eigenvalue problems for a special kind of matrices.Linear Algebra Appl. 416 (2006), 336-347. Zbl 1097.65053, MR 2242733, 10.1016/j.laa.2005.11.017 |
| Reference:
|
[12] Pickmann, H., Egaña, J., Soto, R. L.: Extremal inverse eigenvalue problem for bordered diagonal matrices.Linear Algebra Appl. 427 (2007), 256-271. Zbl 1144.65026, MR 2351358, 10.1016/j.laa.2007.07.020 |
| Reference:
|
[13] Pivovarchik, V., Rozhenko, N., Tretter, C.: Dirichlet-Neumann inverse spectral problem for a star graph of Stieltjes strings.Linear Algebra Appl. 439 (2013), 2263-2292. Zbl 1286.34025, MR 3091304, 10.1016/j.laa.2013.07.003 |
| Reference:
|
[14] Sen, M., Sharma, D.: Generalized inverse eigenvalue problem for matrices whose graph is a path.Linear Algebra Appl. 446 (2014), 224-236. Zbl 1286.65050, MR 3163141, 10.1016/j.laa.2013.12.035 |
| Reference:
|
[15] Sharma, D., Sen, M.: Inverse eigenvalue problems for two special acyclic matrices.Mathematics 4 (2016), Article ID 12, 11 pages. Zbl 1382.65109, 10.3390/math4010012 |
| Reference:
|
[16] Sharma, D., Sen, M.: Inverse eigenvalue problems for acyclic matrices whose graph is a dense centipede.Spec. Matrices 6 (2018), 77-92. Zbl 1391.15098, MR 3764333, 10.1515/spma-2018-0008 |
| Reference:
|
[17] Zhang, Y.: On the general algebraic inverse eigenvalue problems.J. Comput. Math. 22 (2004), 567-580. Zbl 1066.65044, MR 2072173 |
| . |
