Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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COMPUTATIONAL PITFALLS OF HIGH-ORDER METHODS FOR NONLINEAR EQUATIONS

  • Sen, Syamal K. (Department of Mathematical Sciences, Florida Institute of Technology) ;
  • Agarwal, Ravi P. (Department of Mathematics, Texas A & M University-Kingsville) ;
  • Khattri, Sanjay K. (Department of Engineering, Stord-Haugesund University College)
  • Received : 2011.04.28
  • Accepted : 2011.09.02
  • Published : 2012.05.30
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Abstract

Several methods with order higher than that of Newton methods which are of order 2 have been reported in literature for solving nonlinear equations. The focus of most of these methods was to economize on/minimize the number of function evaluations per iterations. We have demonstrated here that there are several computational pit-falls, such as the violation of fixed-point theorem, that one could encounter while using these methods. Further it was also shown that the overall computational complexity could be more in these high-order methods than that in the second-order Newton method.

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References

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