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H. T. Kung and J. F. Traub, “Optimal Order of One-Point and Multipoint Iteration,” Journal of the Association for Computing Machinery, Vol. 21, No. 4, 1974, pp. 643-651. doi: 10.1145/321850.321860

has been cited by the following article:

• TITLE: Improved Ostrowski-Like Methods Based on Cubic Curve Interpolation

  AUTHORS: Janak Raj Sharma, Rangan Kumar Guha, Rajni Sharma

  KEYWORDS: Nonlinear Equations, Ostrowski’s Method, Root-Finding, Order of Convergence, Cubic Interpolation

  JOURNAL NAME: Applied Mathematics, Vol.2 No.7, July 5, 2011

  ABSTRACT: In this paper, we derive two higher order multipoint methods for solving nonlinear equations. The methodology is based on Ostrowski’s method and further developed by using cubic interpolation process. The adaptation of this strategy increases the order of Ostrowski’s method from four to eight and its efficiency index from 1.587 to 1.682. The methods are compared with closest competitors in a series of numerical examples. Moreover, theoretical order of convergence is verified on the examples.