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COMPUTATIONAL PITFALLS OF HIGH-ORDER METHODS FOR NONLINEAR EQUATIONS
Syamal K. Sen,Ravi P. Agarwal,Sanjay K. Khattri 한국전산응용수학회 2012 Journal of applied mathematics & informatics Vol.30 No.3
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.
COMPUTATIONAL PITFALLS OF HIGH-ORDER METHODS FOR NONLINEAR EQUATIONS
Sen, Syamal K.,Agarwal, Ravi P.,Khattri, Sanjay K. The Korean Society for Computational and Applied M 2012 Journal of applied mathematics & informatics Vol.30 No.3
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.