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

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• 作者：Chengyuan He (1)
  Jiangming Ma
  Kunpeng Zhang
  Zhenghua Wang
  
  1. School of Mathematics and Computer Engineering ; Xihua University Chengdu ; Sichuan ; 610039 ; P.R. China
  
• 关键词：r ; circulant matrices ; Fibonacci number ; Lucas number ; spectral norm ; estimation
• 刊名：Journal of Inequalities and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：993 KB
• 参考文献：1. Mathias, R (1990) The spectral norm of a nonnegative matrix. Linear Algebra Appl. 131: pp. 269-284 CrossRef
  2. Solak, S (2005) On the norms of circulant matrices with the Fibonacci and Lucas numbers. Appl. Math. Comput. 160: pp. 125-132 CrossRef
  3. Solak, S (2007) Erratum to 鈥極n the norms of circulant matrices with the Fibonacci and Lucas numbers鈥?[Appl. Math. Comput. 160 (2005) 125-132]. Appl. Math. Comput. 190: pp. 1855-1856 CrossRef
  4. Shen, S, Cen, J (2010) On the bounds for the norms of r-circulant matrices with the Fibonacci and Lucas numbers. Appl. Math. Comput. 216: pp. 2891-2897 CrossRef
  5. Yazlik, Y, Taskara, N (2013) On the norms of an r-circulant matrix with the generalized k-Horadam numbers. J. Inequal. Appl. 2013: CrossRef
  6. Bozkurt, D, Tam, T-Y (2014) Determinants and inverses of r-circulant matrices associated with a number sequence. Linear Multilinear Algebra.
  
• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X

文摘

Let us define \(A=\operatorname{Circ}_{r}(a_{0},a_{1},\ldots,a_{n-1})\) to be a \(n\times n\) r-circulant matrix. The entries in the first row of \(A=\operatorname{Circ}_{r}(a_{0},a_{1},\ldots,a_{n-1})\) are \(a_{i}=F_{i}\) , or \(a_{i}=L_{i}\) , or \(a_{i}=F_{i}L_{i}\) , or \(a_{i}=F_{i}^{2}\) , or \(a_{i}=L_{i}^{2}\) ( \(i=0,1,\ldots,n-1\) ), where \(F_{i}\) and \(L_{i}\) 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.