Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (4): 1066-1078.

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A Class of Efficient Modified Algorithms Based onHalley-Newton Methods

Yajun Xie()   

  1. School of Technology, Fuzhou University of International Studies and Trade & Engineering Research Center of Universities of Fujian Province, Fuzhou 350202
  • Received:2019-12-30 Online:2021-08-26 Published:2021-08-09
  • Supported by:
    the NSF of Fujian Province(2019J01879);the Key Research and Development Projects of University of Chinese Academy of Science H2020003(20A01246ZY);the Major Educational Reform Projects of Fujian Province(FBJG20200310);the High-Level Talents Project of Fuzhou University of International Studies and Trade(FWKQJ2020002)


In this paper, based on the Halley method and the classical Newton method, a class of new modified Halley-Newton method is presented for solving the systems of nonlinear equations with two concrete modified iteration schemes. The convergence performances of the two new variants of Newton iteration method are analyzed in details under appropriate assumptions. Some numerical experiments are given to illustrate the efficiency of the proposed methods.

Key words: Systems of nonlinear equations, Halley method, Newton iteration method, Convergence analysis, Numerical tests

CLC Number: 

  • O224.2