The upper bound estimation on the spectral norm of r-circulant matrices with the Fibonacci and Lucas numbers.

Let us define A = Circr(a0, a1, . . . , an-1) to be a n × n r-circulant matrix. The entries in the first row of A = Circr (a0, a1, . . . , an-1) are ai = Fi, or ai = Li, or ai = FiLi, or ai = F2i, or ai = L2i(i = 0,1, . . . , n - 1),where Fi and Li are the ith Fibonacci and Lucas numbers, respectively. This paper gives an upper bound estimation of the spectral norm for r-circulant matrices with Fibonacci and Lucas numbers. The result is more accurate than the corresponding results of S Solak and S Shen, and of J Cen, and the numerical examples have provided further proof. [ABSTRACT FROM AUTHOR]