On the Norms of r-Hankel Matrices Involving Fibonacci and Lucas Numbers

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DOI: 10.4236/jamp.2018.67117    803 Downloads   1,829 Views  Citations
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ABSTRACT

Let us define A=Hr=(aij) to be n×n r-Hankel matrix. The entries of matrix A are Fn=Fi+j-2 or Ln=Fi+j-2 where Fn and Ln denote the usual Fibonacci and Lucas numbers, respectively. Then, we obtained upper and lower bounds for the spectral norm of matrix A. We compared our bounds with exact value of matrix A’s spectral norm. These kinds of matrices have connections with signal and image processing, time series analysis and many other problems.

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Gökbaş, H. and Köse, H. (2018) On the Norms of r-Hankel Matrices Involving Fibonacci and Lucas Numbers. Journal of Applied Mathematics and Physics, 6, 1409-1417. doi: 10.4236/jamp.2018.67117.
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