A Two-Parameter Family of Fourth-Order Iterative Methods with Optimal Convergence for Multiple Zeros | Zendy

Young Ik Kim | Zendy; Young Hee Geum | Zendy

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A Two-Parameter Family of Fourth-Order Iterative Methods with Optimal Convergence for Multiple Zeros

Author(s) -

Young Ik Kim,

Young Hee Geum

Publication year - 2013

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2013/369067

Subject(s) - mathematics , convergence (economics) , order (exchange) , nonlinear system , constant (computer programming) , derivative (finance) , iterative method , harmonic , mathematical optimization , computer science , physics , finance , quantum mechanics , financial economics , economics , programming language , economic growth

We develop a family of fourth-order iterative methods using the weighted harmonic mean of two derivative functions to compute approximate multiple roots of nonlinear equations. They are proved to be optimally convergent in the sense of Kung-Traub’s optimal order. Numerical experiments for various test equations confirm well the validity of convergence and asymptotic error constants for the developed methods

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