Araştırma Makalesi

On the Norms of Toeplitz Matrices with the Pell, Pell-Lucas and Modified Pell Numbers

Cilt: 1 Sayı: 2 9 Ağustos 2016
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On the Norms of Toeplitz Matrices with the Pell, Pell-Lucas and Modified Pell Numbers

Öz

This paper deals with the usual Pell, Pell-Lucas and Modified Pell numbers and Toeplitz matrices. First, the Toeplitz matrices whose entries are the usual Pell, Pell-Lucas and Modified Pell numbers are constructed, and then the Frobenius, row and column norms of such matrices are computed. Furthermore, the upper and lower bounds for the spectral norms of these matrices are obtained.

Anahtar Kelimeler

Kaynakça

  1. [1] Vajda, Steven. Fibonacci and Lucas numbers, and the golden section: theory and applications. (Courier Corporation, 1989.Koshy, Thomas, 2014).
  2. [2] Koshy, Thomasi. Pell and Pell-Lucas numbers with applications. (New York: Springer, 2014).
  3. [3] Horadam, A. F., “Pell identities.” Fibonacci Quarterly 9 (1971): 245-263.
  4. [4] Horadam, A. F., “Unique minimal representation of integers by negatively subscripted Pell numbers.” The Fibonacci Quarterly 32 (1994): 202-206.
  5. [5] Horadam, A. F., “Applications of modified Pell numbers to representations.” Ulam Quarterly 3(1) (1994): 34-53.
  6. [6] Melham, R., “Sums involving Fibonacci and Pell numbers.” Portugaliae Mathematica 56.3 (1999): 309-318.
  7. [7] Kilic, Emrah, and Dursun Tasci, “The linear algebra of the Pell matrix.” Bol. Soc. Mat. Mexicana, 11 (2005): 3.
  8. [8] Dasdemir, Ahmet, “On the Pell, Pell-Lucas and modified Pell numbers by matrix method.” Applied Mathematical Sciences 5.64 (2011): 3173-3181.

Ayrıntılar

Birincil Dil

İngilizce

Konular

Matematik

Bölüm

Araştırma Makalesi

Yazarlar

Yayımlanma Tarihi

9 Ağustos 2016

Gönderilme Tarihi

4 Mart 2016

Kabul Tarihi

9 Temmuz 2016

Yayımlandığı Sayı

Yıl 2016 Cilt: 1 Sayı: 2

Kaynak Göster

APA
Daşdemir, A. (2016). On the Norms of Toeplitz Matrices with the Pell, Pell-Lucas and Modified Pell Numbers. Journal of Engineering Technology and Applied Sciences, 1(2), 51-57. https://doi.org/10.30931/jetas.283838
AMA
1.Daşdemir A. On the Norms of Toeplitz Matrices with the Pell, Pell-Lucas and Modified Pell Numbers. Journal of Engineering Technology and Applied Sciences. 2016;1(2):51-57. doi:10.30931/jetas.283838
Chicago
Daşdemir, Ahmet. 2016. “On the Norms of Toeplitz Matrices with the Pell, Pell-Lucas and Modified Pell Numbers”. Journal of Engineering Technology and Applied Sciences 1 (2): 51-57. https://doi.org/10.30931/jetas.283838.
EndNote
Daşdemir A (01 Ağustos 2016) On the Norms of Toeplitz Matrices with the Pell, Pell-Lucas and Modified Pell Numbers. Journal of Engineering Technology and Applied Sciences 1 2 51–57.
IEEE
[1]A. Daşdemir, “On the Norms of Toeplitz Matrices with the Pell, Pell-Lucas and Modified Pell Numbers”, Journal of Engineering Technology and Applied Sciences, c. 1, sy 2, ss. 51–57, Ağu. 2016, doi: 10.30931/jetas.283838.
ISNAD
Daşdemir, Ahmet. “On the Norms of Toeplitz Matrices with the Pell, Pell-Lucas and Modified Pell Numbers”. Journal of Engineering Technology and Applied Sciences 1/2 (01 Ağustos 2016): 51-57. https://doi.org/10.30931/jetas.283838.
JAMA
1.Daşdemir A. On the Norms of Toeplitz Matrices with the Pell, Pell-Lucas and Modified Pell Numbers. Journal of Engineering Technology and Applied Sciences. 2016;1:51–57.
MLA
Daşdemir, Ahmet. “On the Norms of Toeplitz Matrices with the Pell, Pell-Lucas and Modified Pell Numbers”. Journal of Engineering Technology and Applied Sciences, c. 1, sy 2, Ağustos 2016, ss. 51-57, doi:10.30931/jetas.283838.
Vancouver
1.Ahmet Daşdemir. On the Norms of Toeplitz Matrices with the Pell, Pell-Lucas and Modified Pell Numbers. Journal of Engineering Technology and Applied Sciences. 01 Ağustos 2016;1(2):51-7. doi:10.30931/jetas.283838

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