Dergiler / Hacettepe Journal of Mathematics and Statistics / 2008 / Cilt: 37 - Sayı: 2

ON THE NORMS OF TOEPLITZ MATRICES INVOLVING FIBONACCI AND LUCAS NUMBERS

Sayfa
89–95
Yayın Tarihi
2022-10-18
DOI
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We have found upper and lower bounds for the spectral norms of these matrices

📌 3 Maddede Bu Makale

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Amaç & Hipotez:Let us define A = [aij ] and B = [bij ] as n × n Toeplitz matrices such that aij ≡ Fi−j and bij ≡ Li−j where F and L denote the usual Fibonacci and Lucas numbers, respectively.
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Temel Bulgular & Veri:Let us define A = [aij ] and B = [bij ] as n × n Toeplitz matrices such that aij ≡ Fi−j and bij ≡ Li−j where F and L denote the usual Fibonacci and Lucas numbers, respectively.
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Sonuç & Katkı:We have found upper and lower bounds for the spectral norms of these matrices
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Lucas numbers · Fibonacci numbers · Toeplitz matrix

Abstract

Let us define A = [aij ] and B = [bij ] as n × n Toeplitz matrices such that aij ≡ Fi−j and bij ≡ Li−j where F and L denote the usual Fibonacci and Lucas numbers, respectively. We have found upper and lower bounds for the spectral norms of these matrices

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Bu Makaleye Atıf Yap

BOZKURT, D., AKBULAK, M. (2022). ON THE NORMS OF TOEPLITZ MATRICES INVOLVING FIBONACCI AND LUCAS NUMBERS. Hacettepe Journal of Mathematics and Statistics, Cilt: 37 - Sayı: 2, 89–95. https://ajindex.com/articles/530727

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Kaynakça (7)

  1. Karaduman, E. An application of Fibonacci numbers in matrices, Applied Mathematics and Computation 147, 903–908, 2004. Kayaba¸s, H. The applications of k-Fibonacci sequences (Sel¸cuk University Graduate School of Natural and Applied Science, Ms Thesis, 2006).
  2. Koshy, T. Fibonacci and Lucas Numbers with Applications (Wiley-Interscience Publications, 2001).
  3. Mathias, R. The spectral norm of nonnegative matrix, Linear Algebra and its Applications 131, 269–284, 1990.
  4. Reams, R. Hadamard inverses, square roots and products of almost semidefinite matrices, Linear Algebra and its Applications 288, 35–43, 1999.
  5. Solak, S. On the norms of circulant matrices with the Fibonacci and Lucas numbers, Applied Mathematics and Computation 160, 125–132, 2005.
  6. Vajda, S. Fibonacci and Lucas Numbers and the Golden Section: Theory and Applications (Ellis Horwood Ltd., 1989).
  7. Zielke, G. Some remarks on matrix norms, condition numbers and error estimates for linear equations, Linear Algebra and its Applications 110, 29–41, 1988.