On a recurrence for permanents of a sequence of 3-tridiagonal matrices

• Autorzy: Trojovský Pavel , Zvoníková Iva

Identyfikatory

DOI

10.17512/jamcm.2019.4.09

• Języki publikacji: EN

Abstrakty

EN

This is a corrigendum of the paper: Küçük, A. Z. & Düz, M. (2017). Relationships between the permanents of a certain type of k-tridiagonal symmetric Toeplitz and the Chebyshev polynomials. Journal of Applied Mathematics and Computational Mechanics, 16, 75-86. We will show that Remark 9, on page 84, does not hold, what is the consequence of the incorrect proof, which authors formulated there.

Słowa kluczowe

EN

permanent; k-tridiagonal matrix; Toeplitz matrix; recurrence relation; Chebyshev polynomial of the second kind

PL

macierz Toeplitza; wielomian Chebyszewa; relacje rekurencyjne; macierz tridiagonalna

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2019
• Tom: Vol. 18, nr 4
• Strony: 95--100
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Trojovský Pavel

• Department of Mathematics, Faculty of Science University of Hradec Královè, Hradec Královè, Czech Republic

autor

Zvoníková Iva

• Department of Mathematics, Faculty of Science University of Hradec Královè, Hradec Královè, Czech Republic

Bibliografia

• [1] El-Mikkawy, M.E.A., & Sogabe, T. (2010). A new family of k-Fibonacci numbers. Appl. Math. Comput., 215, 4456-4461.
• [2] Egerváry, V.E., & Szász, O. (1928). Einige Extremalprobleme im Bereiche der trigonometrischen Polynome. Math. Z., 27(1), 641-652.
• [3] Losonczi, L. (1992). Eigenvalues and eigenvectors of some tridiagonal matrices. Acta Mathematica Hungarica, 60(3), 309-332.
• [4] da Fonseca, C.M. & Kowalenko, V. (2019). Eigenpairs of a family of tridiagonal matrices: three decades later. Acta Math. Hungar.
• [5] Küçük, A.Z., & Düz, M. (2017). Relationships between the permanents of a certain type of k-tridiagonal symmetric Toeplitz and the Chebyshev polynomials. Journal of Applied Mathematics and Computational Mechanics, 16, 75-86.
• [6] Mason, J.C., & Handscomb, D.C. (2003). Chebyshev Polynomials. Boca Raton, USA: Chapman and Hall/CRC Press Company.
• [7] Minc, H. (1978). Permanents. Reading: Addison-Wesley.
• [8] da Fonseca, C.M. (2018). On some conjectures regarding tridiagonal matrices. Journal of Applied Mathematics and Computational Mechanics, 17(4), 13-17.
• [9] https://www.ibm.com/support/knowledgecenter/en/SSFHY8_ 6.1/reference/am5gr_cdst.html
• [10] da Fonseca, C.M. (2011). An identity between the determinant and the permanent of Hessenberg type-matrices. Czechoslovak Mathematical Journal, 61(136), 917-921.
• [11] da Cruz, H. F., Rodrigues, I. I., Serodio, R., Simoes, A., & Velhinho, J. (2017). Convertible Subspaces of Hessenberg-Type Matrices. Mathematics, 5(4), Article number: 79.
• [12] Borowska, A., Łacińska, L., & Rychlewska, J. (2013). On determinant of certain pentadiagonalmatrix. Journal of Applied Mathematics and Computational Mechanics, 12(3), 21-26.
• [13] Borowska, A., Łaci´nska, L., & Rychlewska, J. (2014). A system of linear recurrence equations for determinant of pentadiagonal matrix. Journal of Applied Mathematics and Computational Mechanics, 13(2), 5-12.
• [14] Borowska, A., & Łacińska, L. (2014). Recurrence form for determinant of a heptadiagonal symmetric Toeplitz matrix. Journal of Applied Mathematics and Computational Mechanics, 13, 19-26.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).