TARU PUBLICATIONS
Journal of Discrete Mathematical Sciences and Cryptography cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-0065·ISSN (Print): 0972-0529

Monthly Journal: Publishes theoretical and applied research in all areas of Discrete Mathematical Sciences, Cryptography, Combinatorics, Elliptic Curves and Information Security.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

Computational algorithms for determinant evaluation of cyclic m-diagonal Toeplitz matrices

* ,

* Corresponding author · click or hover a name for details

pp. 1–18Online FirstMay 2026DOI: 10.47974/JDMSC-2592 Crossmark XML
Received:
01 Jul 2025
Published Online:
11 May 2026
Article type:
Research Article
Language:
EN
Article no.:
JDMSC-2592
Pages:
1–18

Abstract

 Cyclic m-diagonal matrices possessing a Toeplitz structure have been extensively studied in the contemporary literature. In this work, we propose two efficient numerical procedures for calculating the determinant of general cyclic m-diagonal matrices possessing a Toeplitz structure. The first procedure is based on converting the matrix into a 2-by-2 block matrix format, subsequently leveraging the inverse of this reformulated matrix. The second technique is based on a conversion to an upper triangular block matrix. The performance of these new algorithms is then benchmarked against established methods from prior research.

Keywords

Subject Classifications

15B0565F4015A15

References

[1] S. Barnett, Matrices: Methods and Applications. Oxford, U.K.: Oxford Univ. Press (1990).
[2] M. Dana and R. Yousefi, “Formulas for the Drazin inverse of matrices with new conditions and its applications,” Int. J. Appl. Comput. Math, vol. 4, no. 4, Art. no. 128 (2018).
[3] G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed. Baltimore, MD, USA: Johns Hopkins Univ. Press (1996).
[4] I. M. Navon, “PENT: A periodic pentadiagonal systems solver,” Commun. Appl. Numer. Methods, vol. 3, no. 1, pp. 63-69 (Jan./Feb. 1987).
[5] J. T. Jia and S. M. Li, “A numerical algorithm for the determinant evaluation of cyclic pentadiagonal matrices with Toeplitz structure,” Numer. Algorithms, vol. 71, no. 2, pp. 337-348 (Feb. 2016).
[6] J. T. Jia and S. M. Li, “On determinants of cyclic pentadiagonal matrices with Toeplitz structure,” Comput. Math. Appl., vol. 73, no. 2, pp. 304-309 (Jan. 2017).
[7] M. Shams Solary and E. Sadeghy, “Determinant for cyclic heptadiagonal matrices with Toeplitz structure,” Afr. Mat., vol. 31, pp. 407-422 (2020).
[8] D. A. H. Ahmed, “On the characteristic polynomial and eigenvalues for block tridiagonal matrices,” J. Discrete Math. Sci. Crypt., vol. 25, no. 6, pp. 1745-1756 (2022).
[9] C. M. da Fonseca, “On some quasi anti-tridiagonal matrices,” J. Discrete Math. Sci. Crypt., vol. 24, no. 4, pp. 1043-1052 (2021).
[10] M. Shams Solary, “Computational properties of pentadiagonal and anti-pentadiagonal block band matrices with perturbed corners,” Soft Comput., vol. 24, pp. 301-309 (2020).
[11] M. Shams Solary, “From matrix polynomial to determinant of block Toeplitz-Hessenberg matrix,” Numer. Algorithms, vol. 94, pp. 1421-1434 (2023).

Views: 141Downloads: 131Citations: 0