Previous |  Up |  Next

Article

Full entry | Fulltext not available (moving wall 24 months)      Feedback
Keywords:
inverse eigenvalue problem; leading principal submatrices; graph of a matrix; eigenpair
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.
References:
[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
[2] Bu, C., Zhou, J., Li, H.: Spectral determination of some chemical graphs. Filomat 26 (2012), 1123-1131. DOI 10.2298/FIL1206123B | MR 3099573 | Zbl 1289.05271
[3] Chu, M. T., Golub, G. H.: Inverse Eigenvalue Problems: Theory, Algorithms, and Applications. Numerical Mathematics and Scientific Computation, Oxford University Press, Oxford (2005). DOI 10.1093/acprof:oso/9780198566649.001.0001 | MR 2263317 | Zbl 1075.65058
[4] Duarte, A. L.: Construction of acyclic matrices from spectral data. Linear Algebra Appl. 113 (1989), 173-182. DOI 10.1016/0024-3795(89)90295-4 | MR 0978591 | Zbl 0661.15024
[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. DOI 10.1137/S089547989631072X | MR 1685042 | Zbl 0929.15008
[6] Ghanbari, K., Parvizpour, F.: Generalized inverse eigenvalue problem with mixed eigendata. Linear Algebra Appl. 437 (2012), 2056-2063. DOI 10.1016/j.laa.2012.05.020 | MR 2950471 | Zbl 1262.15017
[7] Hogben, L.: Spectral graph theory and the inverse eigenvalue problem of a graph. Electron. J. Linear Algebra 14 (2005), 12-31. DOI 10.13001/1081-3810.1174 | MR 2202430 | Zbl 1162.05333
[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. DOI 10.1016/j.laa.2013.01.036 | MR 3034535 | Zbl 1282.05141
[9] Nair, R., Shader, B. L.: Acyclic matrices with a small number of distinct eigenvalues. Linear Algebra Appl. 438 (2013), 4075-4089. DOI 10.1016/j.laa.2012.08.029 | MR 3034516 | Zbl 1282.05142
[10] Nylen, P., Uhlig, F.: Inverse eigenvalue problems associated with spring-mass systems. Linear Algebra Appl. 254 (1997), 409-425. DOI 10.1016/S0024-3795(96)00316-3 | MR 1436689 | Zbl 0879.15007
[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. DOI 10.1016/j.laa.2005.11.017 | MR 2242733 | Zbl 1097.65053
[12] Pickmann, H., Egaña, J., Soto, R. L.: Extremal inverse eigenvalue problem for bordered diagonal matrices. Linear Algebra Appl. 427 (2007), 256-271. DOI 10.1016/j.laa.2007.07.020 | MR 2351358 | Zbl 1144.65026
[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. DOI 10.1016/j.laa.2013.07.003 | MR 3091304 | Zbl 1286.34025
[14] Sen, M., Sharma, D.: Generalized inverse eigenvalue problem for matrices whose graph is a path. Linear Algebra Appl. 446 (2014), 224-236. DOI 10.1016/j.laa.2013.12.035 | MR 3163141 | Zbl 1286.65050
[15] Sharma, D., Sen, M.: Inverse eigenvalue problems for two special acyclic matrices. Mathematics 4 (2016), Article ID 12, 11 pages. DOI 10.3390/math4010012 | Zbl 1382.65109
[16] Sharma, D., Sen, M.: Inverse eigenvalue problems for acyclic matrices whose graph is a dense centipede. Spec. Matrices 6 (2018), 77-92. DOI 10.1515/spma-2018-0008 | MR 3764333 | Zbl 1391.15098
[17] Zhang, Y.: On the general algebraic inverse eigenvalue problems. J. Comput. Math. 22 (2004), 567-580. MR 2072173 | Zbl 1066.65044
Partner of
EuDML logo