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摘要
In Fang et al. (J. Comput. Appl. Math. 220:409-412, 2008), a new two-step predictor-corrector type iterative method free from second derivatives for solving nonlinear equations has been proposed. But if lambda (k) not equal 0, k=1,2,aEuro broken vertical bar aEuro parts per thousand, then their main theorem does not hold. In this note, we first show that the iterative method given by authors has second-order convergence in the case lambda (k) not equal 0, k=1,2,aEuro broken vertical bar aEuro parts per thousand, not the third-order one as claimed in their work. Then, we present a modified scheme to increase the order, and it does not need additional function and derivatives evaluations per iteration. Several examples are given to demonstrate the efficiency and performance of a new modified method. Finally, we further discuss and propose several new modified families of iterative root-finding methods by using a new proposed technique.
- 出版日期2010-5
- 单位南京工业大学; 中国矿业大学（北京）
