COMPUTATIONAL PITFALLS OF HIGH-ORDER METHODS FOR NONLINEAR EQUATIONS
作者： Sanjay K. Khattri , Syamal K. Sen , Ravi P. Agarwal
DOI: 10.14317/JAMI.2012.30.3_4.395
关键词:
摘要: Several methods with order higher than that of Newton which are 2 have been reported in literature for solving nonlinear equations. The focus most these was to economize on/minimize the number function evaluations per iterations. We demonstrated here there several computational pit-falls, such as violation fixed-point theorem, one could encounter while using methods. Further it also shown overall complexity be more high-order second-order method.
koreascience.or.kr参考文章(15)
Sanjay K. Khattri, Altered Jacobian Newton Iterative Method for Nonlinear Elliptic Problems ,(2008)
H. H. H. Homeier, A modified Newton method for root finding with cubic convergence Elsevier (North Holland Publishing Company). ,(2003)
H.H.H. Homeier, On Newton-type methods with cubic convergence Journal of Computational and Applied Mathematics. ,vol. 176, pp. 425- 432 ,(2005) , 10.1016/J.CAM.2004.07.027
R.K. Guha, A family of modified Ostrowski methods with accelerated sixth order convergence Applied Mathematics and Computation. ,vol. 190, pp. 111- 115 ,(2007) , 10.1016/J.AMC.2007.01.009
H. T. Kung, J. F. Traub, Optimal Order of One-Point and Multipoint Iteration Journal of the ACM. ,vol. 21, pp. 643- 651 ,(1974) , 10.1145/321850.321860
E. I., A. M. Ostrowski, Solution of equations and systems of equations Mathematics of Computation. ,vol. 21, pp. 732- ,(1967) , 10.2307/2005025
Amit Kumar Maheshwari, A fourth order iterative method for solving nonlinear equations Applied Mathematics and Computation. ,vol. 211, pp. 383- 391 ,(2009) , 10.1016/J.AMC.2009.01.047
Hongmin Ren, Qingbiao Wu, Weihong Bi, New variants of Jarratt’s method with sixth-order convergence Numerical Algorithms. ,vol. 52, pp. 585- 603 ,(2009) , 10.1007/S11075-009-9302-3
Changbum Chun, YoonMee Ham, Some sixth-order variants of Ostrowski root-finding methods Applied Mathematics and Computation. ,vol. 193, pp. 389- 394 ,(2007) , 10.1016/J.AMC.2007.03.074
Changbum Chun, Some fourth-order iterative methods for solving nonlinear equations Applied Mathematics and Computation. ,vol. 195, pp. 454- 459 ,(2008) , 10.1016/J.AMC.2007.04.105