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J. E. Dennis & R. B. Schnable, “Numerical methods for unconstrained optimization and nonlinear equations,” Prentice-Hall, New York, 1983.

has been cited by the following article:

• TITLE: New Variants of Newton’s Method for Nonlinear Unconstrained Optimization Problems

  AUTHORS: V. KANWAR, Kapil K. SHARMA, Ramandeep BEHL

  KEYWORDS: unconstrained optimization, Newton’s method, order of convergence, power means, initial guess

  JOURNAL NAME: Intelligent Information Management, Vol.2 No.1, January 27, 2010

  ABSTRACT: In this paper, we propose new variants of Newton’s method based on quadrature formula and power mean for solving nonlinear unconstrained optimization problems. It is proved that the order of convergence of the proposed family is three. Numerical comparisons are made to show the performance of the presented methods. Furthermore, numerical experiments demonstrate that the logarithmic mean Newton’s method outperform the classical Newton’s and other variants of Newton’s method. MSC: 65H05.