A numerical algorithm for computing the inverse of a Toeplitz pentadiagonal matrix

• Autorzy: Talibi B. , Hadj D. A. , Sarsri D.

Identyfikatory

DOI

10.17512/jamcm.2018.3.08

• Języki publikacji: EN

Abstrakty

EN

In the current paper, we present a computationally efficient algorithm for obtaining the inverse of a pentadiogonal toeplitz matrix. Few conditions are required, and the algorithm is suited for implementation using computer algebra systems.

Słowa kluczowe

EN

pentadiagonal matrix; Toeplitz matrix; K-Hessenberg matrix; inverse

PL

system algebry komputerowej; macierz K-Hessenberga; odwrotność; inwersja; algorytm numeryczny; macierz Toeplitza

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2018
• Tom: Vol. 17, nr 3
• Strony: 83--95
• Opis fizyczny: Bibliogr. 16 poz., tab.

Twórcy

autor

Talibi B.

• National School of Applied Sciences, Abdelmalek Essaadi University Tangier, Morocco

autor

Hadj D. A.

• Regional Center of the Trades of Education and Training (CRMEF)-Tangier, Avenue My Abdelaziz Souani, BP: 3117, Tangier, Morocco

autor

Sarsri D.

• National School of Applied Sciences, Abdelmalek Essaadi University Tangier, Morocco

Bibliografia

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• [2] Aceto, L., Ghelardoni, P., & Magherini, C. (2012). Boundary value methods for the reconstruction of SturmLiouville potentials. Appl. Math. Comput., 219, 2960-2974; Losiak, J., Neuman, E., & Nowak, J. (1988).The inversion of cyclic tridiagonal matrices. Zastos. Mat., 20(1), 93102.
• [3] Kaya, D. (2003). An explicit and numerical solutions of some fifth-order Kdv equation by decomposition method. Appl. Math. Comput., 144, 353-363.
• [4] El-Sayed, S.M., & Kaya, D. (2004). An application of the ADM to seven order Sawada Kotara equations. Appl. Math. Comput., 157, 93-101.
• [5] Shen, Jie, & Tang, Tao (2006). Spectral and High-Order Methods with Applications. Beijing: Science Press.
• [6] Monterde, J., & Ugail, H. (2006). A general 4th-order PDE method to generate Bezier surfaces from the boundary. Comput. Aided Geom. Design, 23, 208-225.
• [7] Patil, P.G., & Swamy, Y.S. (2008). An eficient model for vibration control by piezoelectric smart structure using finite element method. Eur. J. Comput. Sci. Netw. Secu., 8, 258-264.
• [8] Respondek, J.S. (2011). Numerical recipes for the high efficient inverse of the confluent Vandermonde matrices. Appl. Math. Comput., 218, 2044-2054.
• [9] Respondek, J.S. (2013). Recursive numerical recipes for the high efficient inversion of the confluent Vandermonde matrices. Appl. Math. Comput., 225, 718-730.
• [10] Li, H., & Zhao, D. (2014). An extension of the Golden-Thompson theorem. J. Inequal. Appl.
• [11] Li, H.Y., Gong, Z.G., & Zhao, D. (2014). Least squares solutions of the matrix equation AXB+CYD=E with the least norm for symmetric arrowhead matrices. Appl. Math. Comput., 226, 719-724.
• [12] Wang, Chaojie, Li, Hongyi, & Zhao, Di (2015). An explicit formula for the inverse of a pentadiagonal Toeplitz matrix. Journal of Computational and Applied Mathematics, 278, 12-18.
• [13] Hadj, A., & Elouafi, M. (2008). A fast numerical algorithm for the inverse of a tridiagonal and pentadiagonal matrix. Appl. Math. Comput., 202, 441-445.
• [14] Hadj, D.A., & Elouafi, M. (2008). The characteristic polynomial, eigenvectors and determinant of a pentadiagonal matrix. Appl. Math. Comput., 198(2), 634-642.
• [15] Verde-Star, L. (2015). Elementary triangular matrices and inverses of k-Hessenberg and triangular matrices. Spec. Matrices, 3, 250256.
• [16] Slowik, R. (2018). Inverses and determinants of Toeplitz-Hessenberg matrices. Taiwanese Journal of Mathematics, 22, 4, 901-908

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).