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×n r-circulant matrix A = Circr(a1, a2, . . . , an) and n×n symmetric r-circulant matrix B = SCircr(a1, a2, . . . , an) are ai = Pi or ai = P 2 i or ai = Pi−1 or ai = P 2 i−1, where {Pi}i=0 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.