On The Lagrange Interpolation of Fibonacci Sequence

Penulis

  • Muhammad Syifa'ul Mufid Institut Teknologi Sepuluh Nopember
  • Tahiyatul Asfihani Institut Teknologi Sepuluh Nopember
  • Lukman Hanafi Institut Teknologi Sepuluh Nopember

Kata Kunci:

Fibonacci sequence, Lagrange interpolation

Abstrak

Fibonacci sequence is one of the most common sequences in mathematics. It was first introduced by Leonardo Pisa in his book Liber Abaci (1202). From the first n + 1 terms of Fibonacci sequence, a polynomial of degree at most n can be constructed using Lagrange interpolation. In this paper, we show that this Fibonacci Lagrange Interpolation Polynomial (FLIP) can be obtained both recursively and implicitly.

Referensi

T. Scott and P. Marketos, “On the origin of Fibonacci sequence,” MacTutor History of Mathematics, 2014, also available at www-groups.dcs.st-and.ac.uk/history/Publications/fibonacci.pdf.

A. Benjamin and S. Plott, “A combinatorial approach to fibonomial coefficients,” Fibonacci Quarterly, vol. 46/47, no. 1, 2009.

T. Amdeberhan, X. Chen, V. Moll, and B. Sagan, “Generalized Fibonacci polynomials and fibonomial coefficients,” Annals of Combinatorics, vol. 18, no. 4, pp. 541–562, 2014.

D. Garth, D. Mills, and P. Mitchell, “Polynomials generated by the Fibonacci sequence,” Journal of Integer Sequences, vol. 10, no. 2, p. 3, 2007.

J. Kiusalaas, Numerical methods in engineering with MATLAB

. Cambridge University Press, 2010.

Diterbitkan

2016-09-15

Cara Mengutip

Mufid, M. S., Asfihani, T., & Hanafi, L. (2016). On The Lagrange Interpolation of Fibonacci Sequence. (IJCSAM) International Journal of Computing Science and Applied Mathematics, 2(3), 38–40. Diambil dari https://journal.its.ac.id/index.php/ijcsam/article/view/4607

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