Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2013, Special Issue (2012), Article ID 369067, 7 pages.

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

Young Ik Kim and Young Hee Geum

Full-text: Open access

Abstract

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.

Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2012), Article ID 369067, 7 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394806087

Digital Object Identifier
doi:10.1155/2013/369067

Mathematical Reviews number (MathSciNet)
MR3032258

Zentralblatt MATH identifier
1266.65077

Citation

Kim, Young Ik; Geum, Young Hee. A Two-Parameter Family of Fourth-Order Iterative Methods with Optimal Convergence for Multiple Zeros. J. Appl. Math. 2013, Special Issue (2012), Article ID 369067, 7 pages. doi:10.1155/2013/369067. https://projecteuclid.org/euclid.jam/1394806087


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