On some conjectures regarding tridiagonal matrices

• Autorzy: Fonseca C. M.

Identyfikatory

DOI

10.17512/jamcm.2018.4.02

• Języki publikacji: EN

Abstrakty

EN

We discuss several conjectures proposed recently by A.Z. Küçük and M. Düz on the permanent of certain type of tridiagonal matrices. We recall some less known results on tridiagonal matrices and, at the same time, bring other results together to a common framework.

Słowa kluczowe

EN

tridiagonal matrices; determinant; permanent; Chebyshev polynomials of second kind

PL

macierz trójdiagonalna; wielomiany Czebyszewa; wyznacznik

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2018
• Tom: Vol. 17, nr 4
• Strony: 13--17
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Fonseca C. M.

• Kuwait College of Science and Technology, Doha District, Block 4, P.O. Box 27235, Safat 13133 Kuwait
• University of Primorska, FAMNIT, Glagoljsaˇska 8 6000 Koper, Slovenia

Bibliografia

• [1] Losonczi, L. (1992). Eigenvalues and eigenvectors of some tridiagonal matrices. Acta Matheatica Hungarica, 60, 309-332.
• [2] Losonczi, L. (1987). On some discrete quadratic inequalities. International Series of Numerical Mathematics, 80, 73–85.
• [3] da Fonseca, C.M., & Yılmaz, F. (2015). Some comments on k-tridiagonal matrices: determinant, spectra, and inversion. Applied Mathematics and Computation, 270, 644-647.
• [4] McMillen, T. (2009). On the eigenvalues of double band matrices. Linear Algebra and its Applications, 431, 1890-1897.
• [5] da Fonseca, C.M., & Petronilho, J. (2005). Explicit inverse of a tridiagonal k-Toeplitz matrix. Numerische Mathematik, 100(3), 457-482.
• [6] da Fonseca, C.M., Kouachi, S., Mazilu, D.A., & Mazilu I. (2015). A multi-temperature kinetic Ising model and the eigenvalues of some perturbed Jacobi matrices. Applied Mathematics and Computation, 259, 205-211.
• [7] Borowska, J., & Łaci´nska, L. (2015). Eigenvalues of 2-tridiagonal Toeplitz matrix. Journal of Applied Mathematics and Computational Mechanics, 14, 11-17.
• 8] Borowska, J., Łaci´nska, L., & Rychlewska, J. (2013). On determinant of certain pentadiagonal matrix. Journal of Applied Mathematics and Computational Mechanics, 12, 21-26.
• 9] Küçük, A.Z., & Düz, M. (2017). Relationships between the permanents of a certain type of ktridiagonal symmetric Toeplitz matrix and the Chebyshev polynomials. Journal of Applied Mathematics and Computational Mechanics, 16, 75-86.
• [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] Abramowitz, M., & Stegun, I.A. (1972). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Tenth printing. National Bureau of Standards, Applied Mathematics Series 55.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).