Solution of $x^{2} -nx-1=0$ by Continued Fraction Method and Comparison of the Solution by Newton Raphson Method


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Authors

  • A. Gnanam Department of Mathematics, Government Arts College, Trichy, Tamil Nadu, India
  • S. Krithika Department of Mathematics, Seethalakshmi Ramaswami College, Trichy, Tamil Nadu, India

Keywords:

Continued fractions, Simple continued fraction, Euclidean algorithm, Quadratic irrational, Golden mean, Silver mean, Bisection method, False Position method, Iteration method, Newton -Raphson method

Abstract

In this paper we find the solution of the quadratic equation $x^{2} -nx-1 =0$ using Continued Fraction method and identify the convergence of the solutions with other numerical methods such as Bisection method, False Position method, Iteration method and Newton Raphson method.

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Published

15-06-2018

How to Cite

A. Gnanam, & S. Krithika. (2018). Solution of $x^{2} -nx-1=0$ by Continued Fraction Method and Comparison of the Solution by Newton Raphson Method. International Journal of Mathematics And Its Applications, 6(2 - B), 91–96. Retrieved from http://ijmaa.in/index.php/ijmaa/article/view/705

Issue

Vol. 6 No. 2 - B (2018)

Section

Research Article

License

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.