BOUNDS FOR THE NORMS OF TOEPLITZ MATRICES WITH k-JACOBSTHAL AND kJACOBSTHAL LUCAS NUMBERS
Yıl: 2020 Cilt: 0 Sayı: 45 Sayfa Aralığı: 90 - 100 Metin Dili: İngilizce İndeks Tarihi: 23-02-2021
BOUNDS FOR THE NORMS OF TOEPLITZ MATRICES WITH k-JACOBSTHAL AND kJACOBSTHAL LUCAS NUMBERS
Öz: This work is concerned with the spectral, Euclid norms of Toeplitz matrices with generalized 𝑘-Jacobsthal and k- Jacobsthal Lucas entries. 𝑘- Jacobsthal and k- Jacobsthal Lucas sequences are twogeneralizations of two very popular special integer sequences called Jacobsthal and Jacobsthal Lucassequences. Upper and lower bounds for the spectral norms of these matrices, that is, the matrices ofthe forms 𝐴 = 𝑇 (𝑗𝑘,0,𝑗𝑘,1, … ,𝑗𝑘,𝑛−1 ) and 𝐵 = 𝑇 (𝑐𝑘,0, 𝑐𝑘,1, … , 𝑐𝑘,𝑛−1 ) are obtained. The upperbounds for the Euclidean and spectral norms of Kronecker and Hadamard product matrices of Toeplitzmatrices with k-Jacobsthal and the k- Jacobsthal Lucas numbers are computed.
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- [1] Mathias, R., (1990), The spectral norm of nonnegative matrix, Linear Algebra and its Applications, 131, 269-284.
- [2] Zielke, G., (1988), Some remarks on matrix norms, condition numbers and error estimates for linear equations, Linear Algebra and its Applications, 110, 29-41.
- [3] Reams, R., (1999), Hadamard inverses square roots and products of almost semi-definite matrices, Linear Algebra and its Applications, 288, 35-43.
- [4] Horn, R. A., Johnson, C. R., (1991), Topics in matrix analysis, Cambridge University Press, Cambridge.
- [5] Visick, G., (2000), A quantitative version of the observation that the Hadamard product is a principal submatrix of the Kronecker product, Linear Algebra Appl., 304, 45-68.
- [6] Solak, S., (2005), On the norms of circulant matrices with the Fibonacci and Lucas numbers, Appl. Math. Comput., 160, 125-132.
- [7] Akbulak, M., Bozkurt, D., (2008), On the norms of Toeplitz matrices involving Fibonacci and Lucas numbers, Hacettepe Journal of Mathematics and Statistics, 37(2), 89-95.
- [8] Shen, S., (2012), On the Norms of Toeplitz Matrices Involving k-Fibonacci and k-Lucas Numbers, Int. J. Contemp. Math. Sciences, 7(8), 363-368.
- [9] 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.
- [10] Kocer, E. G., (2007), Circulant, Negacyclic and Semicirculant matrices with the modified Pell, Jacobsthal and Jacobsthal- Lucas numbers, Hacettepe Journal of Mathematics and Statistics, 36(2), 133-142.
- [11] Raza, Z., Ali, M.A., (2015), On the Norms of Some Special Matrices with Generalized Fibonacci Sequence, J. Appl. Math. & Informatics, 33(5–6), 593–605.
- [12] Uygun, S., Eldoğan, H., (2016), The k -Jacobsthal and k -Jacobsthal Lucas sequences, General Mathematics Notes, 36(1), 34-47.
- [13] Uygun, ¸S. , (2016), Some Bounds for the Norms of Circulant Matrices with the k -Jacobsthal and k -Jacobsthal Lucas Numbers, Journal of Mathematics Research, 8(6), 133-138.
APA | UYGUN Ş, AYTAR H (2020). BOUNDS FOR THE NORMS OF TOEPLITZ MATRICES WITH k-JACOBSTHAL AND kJACOBSTHAL LUCAS NUMBERS. , 90 - 100. |
Chicago | UYGUN Şükran,AYTAR Hülya BOUNDS FOR THE NORMS OF TOEPLITZ MATRICES WITH k-JACOBSTHAL AND kJACOBSTHAL LUCAS NUMBERS. (2020): 90 - 100. |
MLA | UYGUN Şükran,AYTAR Hülya BOUNDS FOR THE NORMS OF TOEPLITZ MATRICES WITH k-JACOBSTHAL AND kJACOBSTHAL LUCAS NUMBERS. , 2020, ss.90 - 100. |
AMA | UYGUN Ş,AYTAR H BOUNDS FOR THE NORMS OF TOEPLITZ MATRICES WITH k-JACOBSTHAL AND kJACOBSTHAL LUCAS NUMBERS. . 2020; 90 - 100. |
Vancouver | UYGUN Ş,AYTAR H BOUNDS FOR THE NORMS OF TOEPLITZ MATRICES WITH k-JACOBSTHAL AND kJACOBSTHAL LUCAS NUMBERS. . 2020; 90 - 100. |
IEEE | UYGUN Ş,AYTAR H "BOUNDS FOR THE NORMS OF TOEPLITZ MATRICES WITH k-JACOBSTHAL AND kJACOBSTHAL LUCAS NUMBERS." , ss.90 - 100, 2020. |
ISNAD | UYGUN, Şükran - AYTAR, Hülya. "BOUNDS FOR THE NORMS OF TOEPLITZ MATRICES WITH k-JACOBSTHAL AND kJACOBSTHAL LUCAS NUMBERS". (2020), 90-100. |
APA | UYGUN Ş, AYTAR H (2020). BOUNDS FOR THE NORMS OF TOEPLITZ MATRICES WITH k-JACOBSTHAL AND kJACOBSTHAL LUCAS NUMBERS. Journal of scientific reports-A (Online), 0(45), 90 - 100. |
Chicago | UYGUN Şükran,AYTAR Hülya BOUNDS FOR THE NORMS OF TOEPLITZ MATRICES WITH k-JACOBSTHAL AND kJACOBSTHAL LUCAS NUMBERS. Journal of scientific reports-A (Online) 0, no.45 (2020): 90 - 100. |
MLA | UYGUN Şükran,AYTAR Hülya BOUNDS FOR THE NORMS OF TOEPLITZ MATRICES WITH k-JACOBSTHAL AND kJACOBSTHAL LUCAS NUMBERS. Journal of scientific reports-A (Online), vol.0, no.45, 2020, ss.90 - 100. |
AMA | UYGUN Ş,AYTAR H BOUNDS FOR THE NORMS OF TOEPLITZ MATRICES WITH k-JACOBSTHAL AND kJACOBSTHAL LUCAS NUMBERS. Journal of scientific reports-A (Online). 2020; 0(45): 90 - 100. |
Vancouver | UYGUN Ş,AYTAR H BOUNDS FOR THE NORMS OF TOEPLITZ MATRICES WITH k-JACOBSTHAL AND kJACOBSTHAL LUCAS NUMBERS. Journal of scientific reports-A (Online). 2020; 0(45): 90 - 100. |
IEEE | UYGUN Ş,AYTAR H "BOUNDS FOR THE NORMS OF TOEPLITZ MATRICES WITH k-JACOBSTHAL AND kJACOBSTHAL LUCAS NUMBERS." Journal of scientific reports-A (Online), 0, ss.90 - 100, 2020. |
ISNAD | UYGUN, Şükran - AYTAR, Hülya. "BOUNDS FOR THE NORMS OF TOEPLITZ MATRICES WITH k-JACOBSTHAL AND kJACOBSTHAL LUCAS NUMBERS". Journal of scientific reports-A (Online) 45 (2020), 90-100. |