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http://dx.doi.org/10.14317/jami.2012.30.3_4.395

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)
Publication Information
Journal of applied mathematics & informatics / v.30, no.3_4, 2012 , pp. 395-411 More about this Journal
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.
Keywords
Convergence order; Fixed-point iteration; Newton method; nonlinear equations; optimal iterative methods;
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