A biparametric family of eighth-order methods with their third-step weighting function decomposed into a one-variable linear fraction and a two-variable generic function

  • Authors:

  • Young Hee Geum;Young Ik Kim

  • Affiliations:

  • -;-

  • Venue:
  • Computers & Mathematics with Applications
  • Year:
  • 2011

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Abstract

This paper proposes a biparametric family of three-step eighth-order multipoint iterative methods with optimal efficiency index in the sense of Kung-Traub for simple roots of nonlinear equations. We employ their third-step weighting function decomposed into King's linear fractional function and a two-variable function to construct such a family of optimal methods. Development and convergence analysis on the proposed methods is fully described in addition to numerical experiments including comparison with existing methods.