Note on a cubically convergent Newton-type method under weak conditions (Q970476)

The main result of the paper is contained in Theorem2,where the authors prove that the convergence order of the predictor-corrector type iterative method free from second derivatives proposed by Fang et al. is in general two, not three as claimed in \textit{L. Fang, G. He} and \textit{Z. Hu} [J. Comput. Appl. Math. 220, No.~1--2, 409--412 (2008; Zbl 1146.65042)]. Next, a scheme to increase the convergence order is constructed (in Section 3), several numerical examples are presented (in Section 4). Finally, some multi-steps mathods with higher-order convergence are discussed (in Section 5).