Ball comparison between Jarratt’s and other fourth order method for solving equations

  • Ioannis K. Argyros Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA.
  • Santhosh George Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India.
Keywords: Jarratt method, Banach space, Ball convergence

Abstract

The convergence order of iterative methods is determined using high order derivatives and Taylor series, and without providing computable error bounds, uniqueness of the solution results or information on how to choose the initial point. We address all these problems by using hypotheses only on the first derivative. Moreover, to achieve all these we present our technique using a comparison between the convergence radii of Jarratt’s fourth order method and another method of the same convergence order.

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Published
2019-03-15
How to Cite
Argyros, I. K., & George, S. (2019). Ball comparison between Jarratt’s and other fourth order method for solving equations. CUBO, A Mathematical Journal, 20(3), 65–79. https://doi.org/10.4067/S0719-06462018000300065