Araştırma Makalesi

On the Bounds for the Norms of Toeplitz Matrices with the Jacobsthal and Jacobsthal Lucas Numbers

Cilt: 4 Sayı: 3 31 Aralık 2019
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On the Bounds for the Norms of Toeplitz Matrices with the Jacobsthal and Jacobsthal Lucas Numbers

Öz

In this study, we compute the value of the various norms of the Toeplitz matrices whose elements are Jacobsthal numbers, Jacobsthal Lucas numbers and upper and lower bounds for the spectral norms of these matrices. Also, the Euclidean norm of Kronecker product of Toeplitz matrices with Jacobsthal and the Jacobsthal Lucas numbers are denoted. Finally, the upper bound for the spectral norm of Hadamard product mentioned above matrices are demonstrated.

Anahtar Kelimeler

Kaynakça

  1. [1] Horadam, A.F., “Jacobsthal representation numbers”, The Fibonacci Quarterly 34(1) (1996) : 40-54.
  2. [2] Uygun, S., “The (s, t)-Jacobsthal and (s, t)-Jacobsthal Lucas sequences”, Applied Mathematical Sciences 70(9) (2015) : 3467-3476.
  3. [3] Zielke, G., “Some remarks on matrix norms, condition numbers and error estimates for linear equations”, Linear algebra and its applications 110 (1988) : 29-41.
  4. [4] Mathias, R., “The spectral norm of a nonnegative matrix”, Linear algebra and its applications 139 (1990) : 269-284.
  5. [5] Reams, R., “Hadamard inverses, square roots and products of almost semidefinite matrices”, Linear Algebra and its Applications 288 (1999) : 35-43.
  6. [6] Solak, S., Bozkurt, D., ”On the spectral norms of Cauchy-Toeplitz and Cauchy-Hankel matrices”, Applied Mathematics and Computation 140(2-3) (2003) : 231-238.
  7. [7] Solak, S., “On the norms of circulant matrices with the Fibonacci and Lucas numbers”, Applied Mathematics and Computation 160(1) (2005) : 125-132.
  8. [8] Horn, R.A., Johnson, C.R., “Topics in matrix analysis”, Cambridge University Press, Cambridge, (1991).

Ayrıntılar

Birincil Dil

İngilizce

Konular

Matematik

Bölüm

Araştırma Makalesi

Yayımlanma Tarihi

31 Aralık 2019

Gönderilme Tarihi

24 Mayıs 2019

Kabul Tarihi

9 Kasım 2019

Yayımlandığı Sayı

Yıl 2019 Cilt: 4 Sayı: 3

Kaynak Göster

APA
Uygun, Ş. (2019). On the Bounds for the Norms of Toeplitz Matrices with the Jacobsthal and Jacobsthal Lucas Numbers. Journal of Engineering Technology and Applied Sciences, 4(3), 105-114. https://doi.org/10.30931/jetas.569742
AMA
1.Uygun Ş. On the Bounds for the Norms of Toeplitz Matrices with the Jacobsthal and Jacobsthal Lucas Numbers. Journal of Engineering Technology and Applied Sciences. 2019;4(3):105-114. doi:10.30931/jetas.569742
Chicago
Uygun, Şükran. 2019. “On the Bounds for the Norms of Toeplitz Matrices with the Jacobsthal and Jacobsthal Lucas Numbers”. Journal of Engineering Technology and Applied Sciences 4 (3): 105-14. https://doi.org/10.30931/jetas.569742.
EndNote
Uygun Ş (01 Aralık 2019) On the Bounds for the Norms of Toeplitz Matrices with the Jacobsthal and Jacobsthal Lucas Numbers. Journal of Engineering Technology and Applied Sciences 4 3 105–114.
IEEE
[1]Ş. Uygun, “On the Bounds for the Norms of Toeplitz Matrices with the Jacobsthal and Jacobsthal Lucas Numbers”, Journal of Engineering Technology and Applied Sciences, c. 4, sy 3, ss. 105–114, Ara. 2019, doi: 10.30931/jetas.569742.
ISNAD
Uygun, Şükran. “On the Bounds for the Norms of Toeplitz Matrices with the Jacobsthal and Jacobsthal Lucas Numbers”. Journal of Engineering Technology and Applied Sciences 4/3 (01 Aralık 2019): 105-114. https://doi.org/10.30931/jetas.569742.
JAMA
1.Uygun Ş. On the Bounds for the Norms of Toeplitz Matrices with the Jacobsthal and Jacobsthal Lucas Numbers. Journal of Engineering Technology and Applied Sciences. 2019;4:105–114.
MLA
Uygun, Şükran. “On the Bounds for the Norms of Toeplitz Matrices with the Jacobsthal and Jacobsthal Lucas Numbers”. Journal of Engineering Technology and Applied Sciences, c. 4, sy 3, Aralık 2019, ss. 105-14, doi:10.30931/jetas.569742.
Vancouver
1.Şükran Uygun. On the Bounds for the Norms of Toeplitz Matrices with the Jacobsthal and Jacobsthal Lucas Numbers. Journal of Engineering Technology and Applied Sciences. 01 Aralık 2019;4(3):105-14. doi:10.30931/jetas.569742