Araştırma Makalesi
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On the norms of r-circulant matrices with generalized Fibonacci numbers

Yıl 2017, , 13 - 21, 11.01.2017
https://doi.org/10.13069/jacodesmath.12813

Öz

In this paper, we obtain a generalization of [6, 8]. Firstly, we consider the so-called r-circulant matrices
with generalized Fibonacci numbers and then found lower and upper bounds for the Euclidean
and spectral norms of these matrices. Afterwards, we present some bounds for the spectral norms of
Hadamard and Kronecker product of these matrices.

Kaynakça

  • [1] D. Bozkurt, T. Y. Tam, Determinants and inverses of r􀀀circulant matrices associated with a number sequences, Linear and Multilinear Algebra 63(10) (2015) 2079–2088.
  • [2] H. Civciv, R. Turkmen, Notes on norms of circulant matrices with Lucas numbers, Int. J. Inf. Syst. Sci. 4(1) (2008) 142–147.
  • [3] C. He, J. Ma, K. Zhang, Z. Wang, The upper bound estimation on the spectral norm of r-circulant matrices with the Fibonacci and Lucas numbers, J. Inequal. Appl. Article ID 72 (2015) 1–10.
  • [4] R. A. Horn, C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.
  • [5] R. Mathias, The spectral norm of nonnegative matrix, Linear Algebra Appl. 139 (1990), 269–284.
  • [6] A. Nalli, M. Sen, On the norms of circulant matrices with generalized Fibonacci numbers, Selçuk J. Appl. Math. 11(1) (2010) 107–116.
  • [7] T. Koshy, Fibonacci and Lucas Numbers with Application, John Wiley and Sons, Inc., 2001.
  • [8] S. Shen, J. Cen, On the norms of r􀀀circulant matrices with Fibonacci and Lucas numbers, Appl.
  • [9] S. Solak, On the norms of circulant matrices with Fibonacci and Lucas numbers, Appl. Math. Comput. 160(1) (2005) 125–132.
  • [10] S. Solak, Erratum to "On the norms of circulant matrices with Fibonacci and Lucas numbers" [Appl. Math. Comput. 160(1) (2005) 125-132], Appl. Math. Comput. 190(2) (2007) 1855–1856.
  • [11] N. Tuglu, C. Kizilates, On the norms of circulant and r-circulant matrices with the hyperharmonic Fibonacci numbers, J. Inequal. Appl. Article ID 253 (2015) 1–11.
  • [12] S. Vajda, Fibonacci and Lucas numbers and Golden Section, John Wiley and Sons, Inc., 1989.
Yıl 2017, , 13 - 21, 11.01.2017
https://doi.org/10.13069/jacodesmath.12813

Öz

Kaynakça

  • [1] D. Bozkurt, T. Y. Tam, Determinants and inverses of r􀀀circulant matrices associated with a number sequences, Linear and Multilinear Algebra 63(10) (2015) 2079–2088.
  • [2] H. Civciv, R. Turkmen, Notes on norms of circulant matrices with Lucas numbers, Int. J. Inf. Syst. Sci. 4(1) (2008) 142–147.
  • [3] C. He, J. Ma, K. Zhang, Z. Wang, The upper bound estimation on the spectral norm of r-circulant matrices with the Fibonacci and Lucas numbers, J. Inequal. Appl. Article ID 72 (2015) 1–10.
  • [4] R. A. Horn, C. R. Johnson, Topics in Matrix Analysis, Cambridge University Press, Cambridge, 1991.
  • [5] R. Mathias, The spectral norm of nonnegative matrix, Linear Algebra Appl. 139 (1990), 269–284.
  • [6] A. Nalli, M. Sen, On the norms of circulant matrices with generalized Fibonacci numbers, Selçuk J. Appl. Math. 11(1) (2010) 107–116.
  • [7] T. Koshy, Fibonacci and Lucas Numbers with Application, John Wiley and Sons, Inc., 2001.
  • [8] S. Shen, J. Cen, On the norms of r􀀀circulant matrices with Fibonacci and Lucas numbers, Appl.
  • [9] S. Solak, On the norms of circulant matrices with Fibonacci and Lucas numbers, Appl. Math. Comput. 160(1) (2005) 125–132.
  • [10] S. Solak, Erratum to "On the norms of circulant matrices with Fibonacci and Lucas numbers" [Appl. Math. Comput. 160(1) (2005) 125-132], Appl. Math. Comput. 190(2) (2007) 1855–1856.
  • [11] N. Tuglu, C. Kizilates, On the norms of circulant and r-circulant matrices with the hyperharmonic Fibonacci numbers, J. Inequal. Appl. Article ID 253 (2015) 1–11.
  • [12] S. Vajda, Fibonacci and Lucas numbers and Golden Section, John Wiley and Sons, Inc., 1989.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Makaleler
Yazarlar

Amara Chandoul

Yayımlanma Tarihi 11 Ocak 2017
Yayımlandığı Sayı Yıl 2017

Kaynak Göster

APA Chandoul, A. (2017). On the norms of r-circulant matrices with generalized Fibonacci numbers. Journal of Algebra Combinatorics Discrete Structures and Applications, 4(1), 13-21. https://doi.org/10.13069/jacodesmath.12813
AMA Chandoul A. On the norms of r-circulant matrices with generalized Fibonacci numbers. Journal of Algebra Combinatorics Discrete Structures and Applications. Ocak 2017;4(1):13-21. doi:10.13069/jacodesmath.12813
Chicago Chandoul, Amara. “On the Norms of R-Circulant Matrices With Generalized Fibonacci Numbers”. Journal of Algebra Combinatorics Discrete Structures and Applications 4, sy. 1 (Ocak 2017): 13-21. https://doi.org/10.13069/jacodesmath.12813.
EndNote Chandoul A (01 Ocak 2017) On the norms of r-circulant matrices with generalized Fibonacci numbers. Journal of Algebra Combinatorics Discrete Structures and Applications 4 1 13–21.
IEEE A. Chandoul, “On the norms of r-circulant matrices with generalized Fibonacci numbers”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 4, sy. 1, ss. 13–21, 2017, doi: 10.13069/jacodesmath.12813.
ISNAD Chandoul, Amara. “On the Norms of R-Circulant Matrices With Generalized Fibonacci Numbers”. Journal of Algebra Combinatorics Discrete Structures and Applications 4/1 (Ocak 2017), 13-21. https://doi.org/10.13069/jacodesmath.12813.
JAMA Chandoul A. On the norms of r-circulant matrices with generalized Fibonacci numbers. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017;4:13–21.
MLA Chandoul, Amara. “On the Norms of R-Circulant Matrices With Generalized Fibonacci Numbers”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 4, sy. 1, 2017, ss. 13-21, doi:10.13069/jacodesmath.12813.
Vancouver Chandoul A. On the norms of r-circulant matrices with generalized Fibonacci numbers. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017;4(1):13-21.