On the Spectrum and Spectral Norms of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>r</mml:mi></mml:mrow></mml:math>-Circulant Matrices with Generalized <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>k</mml:mi></mml:mrow></mml:math>-Horadam Numbers Entries

Liu, Lele

doi:10.1155/2014/795175

Cited by 11 publications

(14 citation statements)

References 8 publications

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“…Kocer, Mansour and Tuglu [21] have presented the spectral norms and eigenvalues of circulant matrices whose entries are Horadam numbers. In the same vein, Yazlik and Taskara [22] and Liu [23] obtained new upper and lower bounds for the spectral norms of an r-circulant matrix whose entries are the generalized k-Horadam numbers.…”

Section: Introduction and Historical Backgroundmentioning

confidence: 94%

The $p$-norm of circulant matrices

Bouthat,

Khare,

Mashreghi

et al. 2021

Preprint

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In this note we study the induced p-norm of circulant matrices A(n, ±a, b), acting as operators on the Euclidean space R n . For circulant matrices whose entries are nonnegative real numbers, in particular for A(n, a, b), we provide an explicit formula for the p-norm, 1 ≤ p ≤ ∞. The calculation for A(n, −a, b) is more complex. The 2-norm is precisely determined. As for the other values of p, two different categories of upper and lower bounds are obtained. These bounds are optimal at the end points (i.e. p = 1 and p = ∞) as well as at p = 2.

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Section: Introduction and Historical Backgroundmentioning

confidence: 94%

The $p$-norm of circulant matrices

Bouthat,

Khare,

Mashreghi

et al. 2021

Preprint

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“…Proof. Claim (3) Claim (4) is equivalent to [8,Lemma 5(2)]. Claim (5) is trivial, because the sequence (h n ) is arithmetic.…”

Section: Computation Of C(h) H ≥mentioning

confidence: 99%

“…Our problem is to compute C(h) under suitable assumptions. Recently, Kocer et al [6], İpek [5], Liu [8], and…”

Section: Introductionmentioning

confidence: 99%

The Spectral Norm of a Circulant Matrix

Merikoski¹,

Haukkanen²,

Mattila³

et al. 2018

JPANTA

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“…Lucas, Pell, Pell Lucas, Jacobsthal and Jacobsthal-Lucas sequences, k  Fibonacci and k  Lucas, generalized Fibonacci sequence with two real parameters used non linear recurrence relation, generalized k  Fibonacci and generalized k  Lucas, generalized Fibonacci sequence with four real parameters used non linear recurrence relation, generalized k  Horadam [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

A NOTE ON NEW GENERALIZATIONS OF k-HORADAM SEQUENCES AND THE POWER SEQUENCES OF THESE GENERALIZATIONS

ÇELEMOĞLU

2021

J. Sci. Arts

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In this article, firstly, we have described new generalizations of generalized k - Horadam sequence and we named the generalizations as another generalized k - Horadam sequence {H k,n}nE, a different generalized k - Horadam sequence {qk,n} and an altered generalized k - Horadam sequence {Qk,n) , respectively. Then, we have studied properties of these new generalizations and we have obtained generating function and extended Binet formula for each generalization. Also, we have introduced a power sequence for an altered generalized k - Horadam sequence in order to be used in different applications like number theory, cryptography, coding theory and engineering.

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On the Spectrum and Spectral Norms of r-Circulant Matrices with Generalized k-Horadam Numbers Entries

Cited by 11 publications

References 8 publications

The $p$-norm of circulant matrices

The $p$-norm of circulant matrices

The Spectral Norm of a Circulant Matrix

A NOTE ON NEW GENERALIZATIONS OF k-HORADAM SEQUENCES AND THE POWER SEQUENCES OF THESE GENERALIZATIONS

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