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<p>The local and semi-local convergence of a more stable single-parameter Ostrowski-type method is studied using a single set of assumptions. We used assumptions on the divided difference operators to obtain our analysis. The analysis does not depend on Taylor series expansion as in earlier studies. Thus, we avoid the assumptions on the existence of the sixth-order derivative used in earlier studies. We need the operator to be differentiable up to order two only. Thus, we extended the applicability of the method since the sufficient convergence conditions are weaker. The parameters used in the analysis are verified using an example. Also, a basin of attraction is provided in this study.</p>

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Convergence analysis for a class of Ostrowski-type methods using the properties of divided difference operators

  • 期刊论文

  • 发表日期：

    2026年6月26日

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  • Santhosh George

摘要

The local and semi-local convergence of a more stable single-parameter Ostrowski-type method is studied using a single set of assumptions. We used assumptions on the divided difference operators to obtain our analysis. The analysis does not depend on Taylor series expansion as in earlier studies. Thus, we avoid the assumptions on the existence of the sixth-order derivative used in earlier studies. We need the operator to be differentiable up to order two only. Thus, we extended the applicability of the method since the sufficient convergence conditions are weaker. The parameters used in the analysis are verified using an example. Also, a basin of attraction is provided in this study.