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September 10, 2025European Journal of Mathematical AnalysisOpen Access

On Local and Semi-Local Convergence Analysis of A High-Order Iterative Method for Solving Nonlinear Systems Without High Derivatives

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Authors

IAIoannis K. ArgyrosCameron UniversitySSStepan ShakhnoLviv UniversityYSYurii ShunkinLviv University

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Implication

Analyses local and semi-local convergence in a high-order iterative method for nonlinear systems, suggesting new majorant sequences.

Key Points

  • The proposed method shows convergence of high-order iterations without higher-order derivatives, enhancing efficiency.
  • Local convergence is established under majorant conditions, ensuring solutions are approached effectively across iterations.
  • Semi-local convergence is demonstrated by introducing majorizing sequences, offering a broader applicability of the method.
  • Examples are provided to illustrate theoretical predictions, validating the method's reliability in practice.

Cite This Study

Argyros et al. (2025) studied this question.

synapsesocial.com/papers/68c1ad6354b1d3bfb60e59c1https://doi.org/10.28924/ada/ma.5.18
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Convergence analysis of a class of iterative methods: a unified approach2025
  2. 2Convergence of High-Order Derivative-Free Algorithms for the Iterative Solution of Systems of Not Necessarily Differentiable Equations2024 · 1 citations
  3. 3A One-Parameter Family of Methods with a Higher Order of Convergence for Equations in a Banach Space2024 · 1 citations
  4. 4Derivative free processes of high order for nondifferentiable equations in Banach spaces2024 · 1 citations
  5. 5Extending the Applicability of an Efficient Eighth-Order Method for Solving Equations2026