On the norms of r-circulant matrices with generalized Fibonacci numbers
Keywords:
Matrix norm, r-circulant matrices,, Generalized Fibonacci numbersAbstract
In this paper, we obtain a generalization of [6, 8]. Firstly, we consider the so-called r-circulant matrices with generalized Fibonacci numbers and then found lower and upper bounds for the Euclidean and spectral norms of these matrices. Afterwards, we present some bounds for the spectral norms of Hadamard and Kronecker product of these matrices.
Downloads
References
E. E. Dinc and M. Sen, On the bounds of the norms of some special circulant matrices with the hyper-Fibonacci and Lucas numbers, Adv. Difference Equ. 2014 (2014) Article no. 273.
P. J. Davis, Circulant Matrices, John Wiley & Sons, New York, 1979.
G. H. Golub and C. F. Van Loan, Matrix Computations, 3rd ed., The Johns Hopkins University Press, Baltimore, MD, 1996.
R. A. Horn and C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge, 1985.
R. Mathias, The spectral norm of a nonnegative matrix, Linear Algebra Appl. 139 (1990) 269–284.
A. Nalli and M. Şen, Erratum to “On the norms of circulant matrices with the Fibonacci and Lucas numbers”, Appl. Math. Comput. 188(1) (2007) 1038–1039.
T. Koshy, Fibonacci and Lucas Numbers with Applications, Pure and Applied Mathematics, John Wiley & Sons, New York, 2001.
S. Shen and J. Cen, On the bounds for the norms of $r$–circulant matrices with the Fibonacci and Lucas numbers, Appl. Math. Comput. 216(10) (2010) 2891–2897.
S. Solak, On the norms of circulant matrices with the Fibonacci and Lucas numbers, Appl. Math. Comput. 160(1) (2005) 125–132.
S. Solak, Erratum to “On the norms of circulant matrices with the Fibonacci and Lucas numbers”, Appl. Math. Comput. 190(1) (2007) 1007.
N. Tuglu and C. Kizilates, On the norms of circulant and $r$–circulant matrices with the hyperharmonic Fibonacci numbers, J. Inequal. Appl. 2015 (2015) Article no. 253.
S. Vajda, Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications, Ellis Horwood Series: Mathematics and Its Applications, Ellis Horwood Ltd., Chichester, 1989.