The Matrices of Fibonacci Numbers
نویسنده
چکیده
In a recent paper, Kalman [3] derives many interesting properties of generalized Fibonacci numbers. In this paper, we take a different approach and derive some other interesting properties of matrices of generalized Fibonacci numbers. As an application of such properties, we construct an efficient algorithm for computing matrices of generalized Fibonacci numbers. The topic of generalized Fibonacci sequences discussed here is related to the theory of polyphase sorting in an interesting way; in fact, it is used in optimizing the polyphase sort (see[l] and [7]). The theory of polyphase sorting, in return, helps shape the construction of a fast algorithm for computing the order-fc Fibonacci numbers in 0(k log ri) steps (see [2] and [5]).
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