Some Bounds for the Norms of Circulant Matrices with the k-Jacobsthal and k-Jacobsthal Lucas Numbers
نویسندگان
چکیده
منابع مشابه
Some Bounds for the Norms of Circulant Matrices with the k-Jacobsthal and k-Jacobsthal Lucas Numbers
Abstract In this paper we investigate upper and lower bounds of the norms of the circulant matrices whose elements are k−Jacobsthal numbers and k−Jacobsthal Lucas numbers.
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In this paper we present the sequence of the k-Jacobsthal-Lucas numbers that generalizes the Jacobsthal-Lucas sequence introduced by Horadam in 1988. For this new sequence we establish an explicit formula for the term of order n, the well-known Binet’s formula, Catalan’s and d’Ocagne’s Identities and a generating function. Mathematics Subject Classification 2010: 11B37, 11B83
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Circulant matrix family occurs in various fields, applied in image processing, communications, signal processing, encoding and preconditioner. Meanwhile, the circulant matrices [1, 2] have been extended in many directions recently. The f(x)-circulant matrix is another natural extension of the research category, please refer to [3, 11]. Recently, some authors researched the circulant type matric...
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Abstract In this paper, we consider the k -Fibonacci and k -Lucas sequences {Fk,n}n∈N and {Lk,n}n∈N . Let A = Cr(Fk,0, Fk,1, · · · , Fk,n−1) and B = Cr(Lk,0, Lk,1, · · · , Lk,n−1) be r -circulant matrices. Afterwards, we give upper and lower bounds for the spectral norms of matrices A and B. In addition, we obtain some bounds for the spectral norms of Hadamard and Kronecker products of these ma...
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ژورنال
عنوان ژورنال: Journal of Mathematics Research
سال: 2016
ISSN: 1916-9809,1916-9795
DOI: 10.5539/jmr.v8n6p133