ON THE NORM OF CIRCULANT MATRICES VIA GENERALIZED TETRANACCI NUMBERS

Fatma Yeşil Baran; Tevfik Yetiş

doi:10.35193/bseufbd.662239

ON THE NORM OF CIRCULANT MATRICES VIA GENERALIZED TETRANACCI NUMBERS

Abstract

In this study, the sum of first n terms of this series is formulated by obtaining the Binet formula for the generalized Tetranacci sequence 〖(T〗_n )_(n∈N), whose initial values are T_0=a,〖 T〗_1=b,〖 T〗_2=c,T_3=d and defined by the T_n=pT_(n-1)+qT_(n-2)+rT_(n-3)+sT_(n-4) recurrence relation for n≥4. 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.

Keywords

Circulant Matrix

References

[1] Feinberg, M. (1963). Fibonacci-tribonacci. The Fibonacci Quarterly. 1(1), 71-74.
[2] Waddill, M. E. (1992). The Tetranacci sequence and generalizations. The Fibonacci Quarterly, 30(1), 9-20.
[3] Lind, D. A. (1970). A Fibonacci circulant. The Fibonacci Quarterly, 8(5), 449-455.
[4] Davis, P. J. 1979, Circulant Matrices, John Wiley and Sons, New York.
[5] Öcal, A. A., Tuglu, N., & Altinişik, E. (2005). On the representation of k-generalized Fibonacci and Lucas numbers. Applied mathematics and computation, 170(1), 584-596.
[6] Alptekin, E. G. (2005). Pell, Pell-Lucas ve Modified Pell sayıları ile tanımlı circulant ve semicirculant matrisler (Doctoral dissertation, Selçuk Üniversitesi Fen Bilimleri Enstitüsü).
[7] Solak, S. (2005). On the norms of circulant matrices with the Fibonacci and Lucas numbers. Applied Mathematics and Computation, 160(1), 125-132.
[8] Kocer, E. G., Mansour, T., & Tuglu, N. (2007). Norms of circulant and semicirculant matrices with Horadam's numbers. Ars Combinatoria, 85, 353-359.

[9] Shen, S. Q., & Cen, J. M. (2010). On the spectral norms of r-circulant matrices with the k-Fibonacci and k-Lucas numbers. Int. J. Contemp. Math. Sciences, 5(12), 569-578.
[10] Bahsi, M., & Solak, S. (2014). On the norms of r-circulant matrices with the hyper-Fibonacci and Lucas numbers. J. Math. Inequal, 8(4), 693-705.
[11] Tuglu, N., & Kızılateş, C. (2015). On the norms of circulant and r-circulant matrices with the hyperharmonic Fibonacci numbers. Journal of Inequalities and Applications, 2015(1), 253.
[12] Kızılateş, C., & Tuglu, N. (2018). On the Norms of Geometric and Symmetric Geometric Circulant Matrices with the Tribonacci Number. Gazi University Journal of Science, 31(2), 555-567.
[13] Kızılateş, C., & Tuglu, N. (2016). On the bounds for the spectral norms of geometric circulant matrices. Journal of Inequalities and Applications, 2016(1), 312.
[14] Tuglu, N., & Kızılateş, C. (2015). On the Norms of Some Special Matrices With the Harmonic Fibonacci Numbers. Gazi University Journal of Science, 28(3), 497-501.
[15] Kızılateş, C. (2017). On the Quadra Lucas-Jacobsthal Numbers. Karaelmas Science and Engineering Journal, 7(2), 619-621.
[16] Polatlı, E. On The Bounds For The Spectral Norms Of . r-circulant Matrices With a Type of Catalan Triangle Numbers. Journal of Science and Arts, 48(3), 2019.
[17] Bahşi, M. (2015). On the Norms of Circulant Matrices with the Generalized Fibonacci and Lucas Numbers. TWMS J. Pure Appl. Math. 6(1), 84-92.
[18] Özkoç, A. Ardıyok, E. (2016). Circulant and Negacyclic Matrices Via Tetranacci Numbers. Honam Mathematical J. 38(4), 725-738.
[19] Tascı, D., & Acar, H. (2017). Gaussian tetranacci numbers. Communications in Mathematics ans Applications, 8(3), 379-386.
[20] Horadam, A. F. (1965). Basic properties of a certain generalized sequence of numbers. The Fibonacci Quarterly, 3(3), 161-176.
[21] Karner, H., Schneid, J., & Ueberhuber, C. W. (2003). Spectral decomposition of real circulant matrices. Linear Algebra and Its Applications, 367, 301-311.
[22] Pollock, D. S. G. (2002). Circulant matrices and time-series analysis. International Journal of Mathematical Education in Science and Technology, 33(2), 213-230.
[23] Zaveri M. N. , Patel, J. K. (2015). Patel J. K. Binet’s Formula for the Tetranacci Sequence. International Journal of Science and Research (IJSR), 78-96.
[24] Spickerman, W.R. (1982). Binet's formula for the Tribonacci sequence, The Fibonacci Quarterly. 20 (2), 118-120.

Details

Primary Language

English

Subjects

Engineering

Journal Section

Research Article

Authors

Fatma Yeşil Baran ^*
0000-0001-8613-2706
Türkiye

Tevfik Yetiş
0000-0002-7835-3178
Türkiye

Publication Date

December 26, 2019

Submission Date

December 20, 2019

Acceptance Date

December 23, 2019

Published in Issue

Year 2019 Volume: 6 Number: 2

DOI

https://doi.org/10.35193/bseufbd.662239

IZ

https://izlik.org/JA36PF47HF

Cite

RIS / Bibtex

APA

Yeşil Baran, F., & Yetiş, T. (2019). ON THE NORM OF CIRCULANT MATRICES VIA GENERALIZED TETRANACCI NUMBERS. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, 6(2), 562-572. https://doi.org/10.35193/bseufbd.662239

AMA

1.Yeşil Baran F, Yetiş T. ON THE NORM OF CIRCULANT MATRICES VIA GENERALIZED TETRANACCI NUMBERS. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi. 2019;6(2):562-572. doi:10.35193/bseufbd.662239

Chicago

Yeşil Baran, Fatma, and Tevfik Yetiş. 2019. “ON THE NORM OF CIRCULANT MATRICES VIA GENERALIZED TETRANACCI NUMBERS”. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi 6 (2): 562-72. https://doi.org/10.35193/bseufbd.662239.

EndNote

Yeşil Baran F, Yetiş T (December 1, 2019) ON THE NORM OF CIRCULANT MATRICES VIA GENERALIZED TETRANACCI NUMBERS. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi 6 2 562–572.

IEEE

[1]F. Yeşil Baran and T. Yetiş, “ON THE NORM OF CIRCULANT MATRICES VIA GENERALIZED TETRANACCI NUMBERS”, Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, vol. 6, no. 2, pp. 562–572, Dec. 2019, doi: 10.35193/bseufbd.662239.

ISNAD

Yeşil Baran, Fatma - Yetiş, Tevfik. “ON THE NORM OF CIRCULANT MATRICES VIA GENERALIZED TETRANACCI NUMBERS”. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi 6/2 (December 1, 2019): 562-572. https://doi.org/10.35193/bseufbd.662239.

JAMA

1.Yeşil Baran F, Yetiş T. ON THE NORM OF CIRCULANT MATRICES VIA GENERALIZED TETRANACCI NUMBERS. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi. 2019;6:562–572.

MLA

Yeşil Baran, Fatma, and Tevfik Yetiş. “ON THE NORM OF CIRCULANT MATRICES VIA GENERALIZED TETRANACCI NUMBERS”. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi, vol. 6, no. 2, Dec. 2019, pp. 562-7, doi:10.35193/bseufbd.662239.

Vancouver

1.Fatma Yeşil Baran, Tevfik Yetiş. ON THE NORM OF CIRCULANT MATRICES VIA GENERALIZED TETRANACCI NUMBERS. Bilecik Şeyh Edebali Üniversitesi Fen Bilimleri Dergisi. 2019 Dec. 1;6(2):562-7. doi:10.35193/bseufbd.662239

Cited By

Genelleştirilmiş tetranacci sayıları ile tanımlı circulant matrislerin özdeğerleri

Gümüşhane Üniversitesi Fen Bilimleri Enstitüsü Dergisi

https://doi.org/10.17714/gumusfenbil.830575

On Generalized Commutative Quaternions with Generalized Tetranacci Number Components

Karaelmas Science and Engineering Journal

https://doi.org/10.7212/karaelmasfen.1359322