The Rule of Hessenberg Matrix for Computing Determinant of Centrosymmetric Matrices

Nur Khasanah, Agustin Absari Wahyu Kuntarini

Abstract


The application of centrosymmetric matrix on engineering take their part, particulary about determinat rule. This basic rule needs computational process for determining appropiate algorithm. Therefore, by the algorithm of determinant kind of Hessenberg matrix, this is used for computing determinant of centrosymmetric matrix more efficiently. This paper shows the algorithm of lower Hessenberg and sparse Hessenberg matrix to construct the efficient alforithm of determinant of centrosymmetric matrix. By using the special structure of centrosymmetric matrix, the algorithm of these determinant are usefull for their own characterstics.

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References


Datta and Morgera, "On the reducibility of centrosymmetric matrices-Aplication in engineering problems", Circuits System Signal Process., 8 (1) pp. 71-95, 1989.

Zhong-Yun Liu, "Some properties of centrosymmetric matrices", Appl. Math. Comput. 141 pp. 297-306, 2003.

Gene H. Golub and Charles F. Van Loan, "Matrix Computations, third ed.", Johns Hopkins University Press, Baltimore and London, (1996).

Y.-H. Chen, C.-Y. Yu, A new algorithm for computing the inverse and the determinant of a Hessenberg matrix, Appl. Math. Comput. 218 (2011) 4433–4436.

Tomohiro Sogabe, "On a two-term recurrence for the determinant of a general matrix", Appl. Math. Comput., 187 pp. 785-788, 2007.

Mohamed Elouafi and A.D. Aiat Hadj, "A new recursive algorithm for inverting Hessenberg matrices", Appl. Math. Comput., 214 pp. 497-499, 2009.

Di Zhao and Hongyi Li, "On the computation of inverse and determinant of a kind of special matrices", Appl. Math. Comput., 250 pp. 721-726, 2015.

N Khasanah, Farikhin and B Surarso, "The algorithm of determinant of centrosymmetric matrix based on lower Hessenberg form", IOP Conf. Series : Journal of Physics : Conf. Series 824 ,2017.

Nur Khasanah, Bayu Surarso, and Farikhin, “Necessary and sufficient on the computation of determinant of a kind of special matrix”, AIP Conference Proceedings 2234, 040014, 2020.

Tomohiro Sogabe, “A fast numerical algorithm for the determinant of a pentadiagonal matrix”, Appl. Math. Comput., 196 pp. 835-841, 2008.

Abderraman Marrero and V Tomeo, “Some results on determinants and inverses of nonsingular pentadiagonal matrices”, J. Comput. Appl. Math., 275 pp. 447-455, 2015.

Zheng Wang, ”The inverse and the determinant of pentadiagonal Toeplitz matrix”, IJSM, 5(3) pp. 28-31 2018.

Jiteng Jia, Boting Yang and Sumei Li, “On a homogenous reccurence relation for the determinants of general pentadiagonal Toeplitz matrices”, Comp. Math Appl., 71 pp. 1036-1044, 2016.

Jiteng Jia and Sumei Li, “On determinants of cyclic pentadiagonal matrices with Toeplitz structure”, Comp. Math Appl., 73 pp. 304-309, 2017.

Jolanta Borowska, Lena Lacinska and Jowita Rychlewska, “On determinant of certain pentadiagonal matrix”, J. Appl. Math. Comput. Mech., 12(3) pp21-26, 2013.

D.J. Evans, A recursive algorithm for determining the eigenvalues of a quindiagonal matrix, Comput. J. 18 (1973) 70–73.

R.A. Sweet, A recursive relation for the determinant of a pentadiagonal matrix, Comm. ACM 12 (1969) 330–332.




DOI: https://doi.org/10.18860/ca.v6i3.9939

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