On Newton-type methods with cubic convergence
作者： H.H.H. Homeier
DOI: 10.1016/J.CAM.2004.07.027
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摘要: Recently, there has been some progress on Newton-type methods with cubic convergence that do not require the computation of second derivatives. Weerakoon and Fernando (Appl. Math. Lett. 13 (2000) 87) derived Newton method a cubically convergent variant by rectangular trapezoidal approximations to Newton's theorem, while Frontini Sormani (J. Comput. Appl. 156 (2003) 345; 140 419 further variants using different theorem. Homeier 157 227; 169 (2004) 161) independently one latter extended it multivariate case. Here, we show can modify Werrakoon-Fernando approach theorem for inverse function derive new class methods.
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