Note on a cubically convergent Newton-type method under weak conditions. (English) Zbl 1198.41010
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 L. Fang, G. He and 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).
Reviewer: Dan Bārbosu (Baia Mare)
MSC:
| 41A25 | Rate of convergence, degree of approximation |
Keywords:
nonlinear equation; iterative method; Newton’s method; order of convergence; approximated functionCitations:
Zbl 1146.65042References:
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