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

作者：Geum Young Hee; Kim Young Ik^*

来源：Computers & Mathematics with Applications, 2011, 61(3): 708-714.

DOI：10.1016/j.camwa.2010.12.020

• Eighth-order convergence
• Efficiency index
• Biparametric family
• Asymptotic error constant
• Weighting function
• Multipoint method

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.

• 出版日期2011-2