On the circulant matrices with Ducci sequence and Gaussian Fibonacci numbers

2021 ◽  
Author(s):  
Roji Bala ◽  
Vinod Mishra
Keyword(s):  
Fibonacci Numbers ◽  
Circulant Matrices

scholarly journals A New Method of Matrix Decomposition to Get the Determinants and Inverses of r -Circulant Matrices with Fibonacci and Lucas Numbers

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Jiangming Ma ◽  
Tao Qiu ◽  
Chengyuan He
Keyword(s):  
Fibonacci Numbers ◽  
Matrix Decomposition ◽  
Circulant Matrix ◽  
New Method ◽  
Circulant Matrices ◽  
Computational Time ◽  
Lucas Numbers ◽  
Fibonacci And Lucas Numbers

We use a new method of matrix decomposition for r -circulant matrix to get the determinants of A n = Circ r F 1 , F 2 , … , F n and B n = Circ r L 1 , L 2 , … , L n , where F n is the Fibonacci numbers and L n is the Lucas numbers. Based on these determinants and the nonsingular conditions, inverse matrices are derived. The expressions of the determinants and inverse matrices are represented by Fibonacci and Lucas Numbers. In this study, the formulas of determinants and inverse matrices are much simpler and concise for programming and reduce the computational time.

scholarly journals On the circulant matrices with Ducci sequences and Fibonacci numbers

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5501-5508
Author(s):  
Süleyman Solak ◽  
Mustafa Bahşi ◽  
Osman Kan
Keyword(s):  
Fibonacci Numbers ◽  
Circulant Matrix ◽  
Circulant Matrices

A Ducci sequence generated by A = (a1,a2,...,an)? Zn is the sequence {A,DA,D2A,...} where the Ducci map D : Zn ? Zn is defined by D(A) = D(a1, a2,...,an) = (|a2-a1|, |a3-a2|,..., |an-an-1|, |an-a1|). In this study, we examine some properties of the matrices Cn, DCn, D2Cn; where Cn =Circ(c0,c1,..., cn-1) is a circulant matrix whose entries consist of Fibonacci numbers.

scholarly journals Determinants and inverses of circulant matrices with complex Fibonacci numbers

2015 ◽  
Vol 3 (1) ◽  
Author(s):  
Ercan Altınışık ◽  
N. Feyza Yalçın ◽  
Şerife Büyükköse
Keyword(s):  
Fibonacci Numbers ◽  
Circulant Matrices

AbstractLet ℱ

scholarly journals The Identical Estimates of Spectral Norms for Circulant Matrices with Binomial Coefficients Combined with Fibonacci Numbers and Lucas Numbers Entries

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Jianwei Zhou
Keyword(s):  
Fibonacci Numbers ◽  
Circulant Matrices ◽  
Binomial Coefficients ◽  
Lucas Numbers ◽  
Numerical Tests

Improved estimates for spectral norms of circulant matrices are investigated, and the entries are binomial coefficients combined with either Fibonacci numbers or Lucas numbers. Employing the properties of given circulant matrices, this paper improves the inequalities for their spectral norms, and gets corresponding identities of spectral norms. Moreover, by some well-known identities, the explicit identities for spectral norms are obtained. Some numerical tests are listed to verify the results.

scholarly journals On Skew Circulant Type Matrices Involving Any Continuous Fibonacci Numbers

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Zhaolin Jiang ◽  
Jinjiang Yao ◽  
Fuliang Lu
Keyword(s):  
Fibonacci Numbers ◽  
Spectral Norm ◽  
Matrix Norm ◽  
Circulant Matrices ◽  
Frobenius Norm ◽  
Transformation Matrices ◽  
Skew Circulant

Circulant and skew circulant matrices have become an important tool in networks engineering. In this paper, we consider skew circulant type matrices with any continuous Fibonacci numbers. We discuss the invertibility of the skew circulant type matrices and present explicit determinants and inverse matrices of them by constructing the transformation matrices. Furthermore, the maximum column sum matrix norm, the spectral norm, the Euclidean (or Frobenius) norm, and the maximum row sum matrix norm and bounds for the spread of these matrices are given, respectively.

On a system of three difference equations of higher order solved in terms of Lucas and Fibonacci numbers

2020 ◽  
Vol 70 (3) ◽  
pp. 641-656
Author(s):  
Amira Khelifa ◽  
Yacine Halim ◽  
Abderrahmane Bouchair ◽  
Massaoud Berkal
Keyword(s):  
General Solution ◽  
Closed Form ◽  
Difference Equations ◽  
Fibonacci Numbers ◽  
Higher Order ◽  
Real Numbers ◽  
Lucas Numbers ◽  
Rational Difference Equations ◽  
Initial Values ◽  
Fibonacci And Lucas Numbers

AbstractIn this paper we give some theoretical explanations related to the representation for the general solution of the system of the higher-order rational difference equations$$\begin{array}{} \displaystyle x_{n+1} = \dfrac{1+2y_{n-k}}{3+y_{n-k}},\qquad y_{n+1} = \dfrac{1+2z_{n-k}}{3+z_{n-k}},\qquad z_{n+1} = \dfrac{1+2x_{n-k}}{3+x_{n-k}}, \end{array}$$where n, k∈ ℕ0, the initial values x−k, x−k+1, …, x0, y−k, y−k+1, …, y0, z−k, z−k+1, …, z1 and z0 are arbitrary real numbers do not equal −3. This system can be solved in a closed-form and we will see that the solutions are expressed using the famous Fibonacci and Lucas numbers.

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