On the norms of r-circulant matrices with the hyper-Fibonacci and Lucas numbers

Bahşi, Mustafa; Solak, Süleyman

doi:10.7153/jmi-08-52

Cited by 22 publications

(9 citation statements)

References 10 publications

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“…Bahşi calculated the matrix norms of circulant matrices consisting of elements of the Tribonacci sequence by changing the initial conditions of the generalized Fibonacci and Lucas numbers [17].…”

Section: Introductionmentioning

confidence: 99%

On the Norm of Circulant Matrices via Generalized Tetranacci Numbers

Baran¹,

Yetiş²

2019

Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi

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ÖZBu çalışmada başlangıç değerleri = , = , = , = olan ve ≥ için,rekürans bağıntısı ile tanımlanan ( ) ∈ℕ Genelleştirilmiş Tetranacci Dizisi için Binet formülü elde edilerek, bu dizinin ilk teriminin toplamı formülüze edilmiştir. Genelleştirilmiş Tetranacci sayı dizisi için üreteç fonksiyonuna ulaşılmıştır. Ayrıca elemanları genelleştirilmiş Tetranacci sayı dizisinin elemanlarından oluşan circulant matrisler için bazı matris normları hesaplanmıştır. ABSTRACTIn this study, the sum of first terms of this series is formulated by obtaining the Binet formula for the generalized Tetranacci sequence ( ) ∈ℕ , whose initial values are = , = , = , = and defined by therecurrence relation for ≥ . The generating function is obtained for generalized Tetranacci number sequence. In addition, some matrix norms are calculated for the circulant matrices consisting of elements of the generalized Tetranacci number sequence.

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Section: Introductionmentioning

confidence: 99%

On the Norm of Circulant Matrices via Generalized Tetranacci Numbers

Baran¹,

Yetiş²

2019

Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi

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“…In [10], Can and Naim have defined geometric circulant matrices and studied the bounds for the spectral norms of geometric circulant matrices involving the generalized Fibonacci number and Lucas numbers. Some great contributions for the spectral norms of r -circulant matrix and geometric circulant matrix can be found in references [11–17]. In particular, Köme and Yazlik [11] have presented new upper and lower bounds for the spectral norms of the r -circulant matrices with biperiodic Fibonacci and biperiodic Lucas numbers, , and , then they gave the lower and upper bounds for the spectral norms of Kronecker and Hadamard products of the matrices Q and L .…”

Section: Introductionmentioning

confidence: 99%

The spectral norms of geometric circulant matrices with the generalized k-Horadam numbers

Shi

2018

J Inequal Appl

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In this paper, we use the algebra methods, the properties of the r-circulant matrix and the geometric circulant matrix to study the upper and lower bound estimate problems for the spectral norms of a geometric circulant matrix involving the generalized k-Horadam numbers, and we obtain some sharp estimations for them. We can also give a new estimation for the norms of a r-circulant matrix involving the generalized k-Horadam numbers.

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“…Bahşi [1] have already studied this question. We will survey their results in Section 2 and give further results in Sections 3 and 4.…”

Section: Introductionmentioning

confidence: 99%