The upper bound estimation for the spectral norm of r-circulant and symmetric r-circulant matrices with the Padovan sequence

In this paper, we gives an upper bound estimation of the spectral norm for matrices A and B such that the entries in the first row of n x n r-circulant matrix A = Circ(r)(a(1), a(2),..., a(n)) and n x n symmetric r-circulant matrix B = SCirc(r)(a(1), a(2),..., a(n)) are a(i) = P-i or a(i), = P-i(2) or a(i) = Pi-1 or a(i) = P-i-1(2), where {P-i}(i=0)(infinity) is Padovan sequence. At the last section, some illustrative numerical example is furnished which demonstrate the validity of the hypotheses and degree of utility of our results. (C) 2016 All rights reserved.