## 14 Citations

Improved algorithms for the calculation of Fibonacci numbers

- Computer Science, Engineering
- 2008

New algorithms that compute Fibonacci numbers, having complexity less than log based on recursive algorithms, are presented, all in tail-recursive form so they can easily be converted to their iterative form.

Middle and Ripple, fast simple O(lg n) algorithms for Lucas Numbers

- Computer ScienceArXiv
- 2010

A fast simple O(\log n) iteration algorithm for individual Lucas numbers is given. This is faster than using Fibonacci based methods because of the structure of Lucas numbers. Using a sqrt 5…

Computing Fibonacci Numbers Fast using the Chinese Remainder Theorem

- Mathematics
- 2003

The purpose of this paper is to investigate the calculation of Fibonacci numbers using the Chinese Remainder Theorem (CRT). This paper begins by laying down some general conclusions that can be made…

Golden and Alternating, fast simple O(lg n) algorithms for Fibonacci

- Computer ScienceArXiv
- 2010

Two very fast and simple O(lg n) algorithms for individual Fibonacci numbers are given and compared to competing algorithms. A simple O(lg n) recursion is derived that can also be applied to Lucas. A…

On the computing of the generalized order-k Pell numbers in log time

- Mathematics, Computer ScienceAppl. Math. Comput.
- 2006

A Simple and Fast Algorithm for Computing the N-th Term of a Linearly Recurrent Sequence

- Computer Science, MathematicsSOSA
- 2021

A simple and fast algorithm for computing the N-th term of a given linearly recurrent sequence and several algorithmic applications, notably to polynomial modular exponentiation, powering of matrices and high-order lifting are discussed.

THE FIBONACCI QUARTERLY

- Mathematics
- 2010

. By interpreting various sums involving Fibonacci and Lucas numbers physically, we show how one can often generate an additional summation with little eﬀort. To illustrate the fruitfulness of the…

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The Art in Computer Programming

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Here the authors haven’t even started the project yet, and already they’re forced to answer many questions: what will this thing be named, what directory will it be in, what type of module is it, how should it be compiled, and so on.

Computing fibonacci numbers quickly

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Computing Fibonacci Numbers (and Similarly Defined Functions) in Log Time

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Derivation of an O(k² log n) Algorithm for Computing Order-k Fibonacci Numbers From the O(k³ log n) Matrix Multiplication Method

- Computer ScienceInf. Process. Lett.
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An Iterative Program to Calculate Fibonacci Numbers in O(log n) Arithmetic Operations

- MathematicsInf. Process. Lett.
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An O(log n) Algorithm for Computing the nth Element of the Solution of a Difference Equation

- Computer ScienceInf. Process. Lett.
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