On a numerical approach to compute the powers of doubly Leslie matrices using Fibonacci-Horner decomposition and determinantal form
*Amal AlouiCorresponding authoramal.alaoui@uit.ac.maDepartment of Mathematics Faculty of Sciences University of Ibn Tofail Kénitra, Morocco0000-0002-7535-1652View full profile → , Mustapha Rachidimustapha.rachidi@ufms.brInstitute of Mathematics INMA, Federal University of Mato Grosso do Sul UFMS, Campo GrandeIntitut of Mathematics Universidade Federal de Mato Grosso do Sul Campo GrandeMato Grosso do Sul, 79070-900, MS- Brazil0000-0002-8210-7383View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 05 Nov 2024
- Published Online:
- 17 Jan 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2229
- Pages:
- 809–823
Abstract
Keywords
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References
[1] J. A. Marrero, R. Bentaher, and M. Rachidi, “On explicit formulas for the principal matrix logarithm,” Appl. Math. Comput., vol. 220, pp. 142–148 (2013).
[2] D. A. Hadj Ahmed, A. Bentaleb, M. Rachidi, and F. Zitan, “Powers of matrices by density and divided differences,” Int. J. Algebra, vol. 3, no. 9, pp. 407–422 (2009).
[3] A. Aloui, M. Rachidi, and B. El Wahbi, “On a numerical approach for the powers of the doubly leslie and doubly companion matrices with applications,” Comput. Sci., vol. 16, no. 2, pp. 613–638 (2021).
[4] A. Aloui and M. Rachidi, “On the computational and numerical approaches for the powers of the doubly Lefkovitch matrix by linear difference equations,” J. Math. Comput. Sci., vol. 31, no. 3, pp. 287–304 (2023).
[5] R. Ben Taher, M. Mouline, and M. Rachidi, “Fibonacci-Horner decomposition of the matrix exponential and the fundamental system of solutions,” Electron. J. Linear Algebra, vol. 15, pp. 178–190 (2006).
[6] R. Ben Taher, N. Naassi, and M. Rachidi, “On the Leslie matrices, Fibonacci sequences and population dynamics,” J. Discrete Math. Sci. Cryptogr., vol. 20, no. 2, pp. 565–594 (2017).
[7] B. N. Datta and K. Datta, “An algorithm for computing powers of a Hessenberg matrix and its applications,” Linear Algebra Appl., vol. 14, no. 3, pp. 273–284 (1976).
[8] F. R. Gantmacher, The Theory of Matrices, vol. 1. New York, NY, USA: Chelsea (1959).
[9] F. R. Gantmacher, Applications of the Theory of Matrices, vol. 2. New York, NY, USA: Interscience (1959).
[10] T. Goy and M. Shattuck, “Determinant formulas of some Hessenberg matrices with Jacobsthal entries,” Appl. Appl. Math. Int. J., vol. 16, no. 1, Art. no. 10 (2021).
[11] R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge, U.K.: Cambridge Univ. Press (1997).
[12] R. K. Kittappa, “A representation of the solution of the nth order linear difference equation with variable coefficients,” Linear Algebra Appl., vol. 193, pp. 211–222 (1993).
[13] H. Kıyak, F. Yılmaz, and D. Bozkurt, “A formula for computing integer powers for one type of tridiagonal matrix,” Hacet. J. Math. Stat., vol. 39, no. 3, pp. 351–363 (2010).
[14] M. Mouline and M. Rachidi, “Application of Markov chains properties to r-generalized Fibonacci sequences,” Fibonacci Quart., vol. 37, no. 1, pp. 34–38 (1999).
[15] M. Mouline and M. Rachidi, “Suites de Fibonacci généralisées, Théorème de Cayley–Hamilton et Chaines de Markov,” Rend. Semin. Mat. Messina, Ser. II, vol. 4, no. 19, pp. 107–115 (1996/97).
[16] T. Muir, The Theory of Determinants in the Historical Order of Development, vol. 3. New York, NY, USA: Dover (1960).
[17] H. Pickmann-Soto, S. Arela-Perez, H. Nina, and E. Valero, “Inverse maximal eigenvalues problems for Leslie and doubly Leslie matrices,” Linear Algebra Appl., vol. 592, pp. 93–112 (2020).
[18] L. Verde-Star, “Functions of matrices,” Linear Algebra Appl., vol. 406, pp. 285–300 (2005).
[19] W. Wanicharpichat, “Explicit minimum polynomial, eigenvector and inverse formula of doubly Leslie matrix,” J. Appl. Math. Inform., vol. 33, no. 3-4, pp. 247–260 (2015).
