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<p>This paper presents a convergence analysis of a family of third-order iterative methods within continuous and differentiable vector fields on Riemannian manifold. We establish conditions under which these methods converge, highlighting their applicability in complex geometrical settings. As illustrative examples, we examine the Chen system and Liu system, demonstrating how these numerical cases support our theoretical findings.</p>

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Convergence analysis of higher order iterative methods in Riemannian manifold

  • 期刊论文

  • 发表日期：

    2025年10月16日

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  • Babita Mehta,
  • P. K. Parida,
  • Sapan Kumar Nayak

摘要

This paper presents a convergence analysis of a family of third-order iterative methods within continuous and differentiable vector fields on Riemannian manifold. We establish conditions under which these methods converge, highlighting their applicability in complex geometrical settings. As illustrative examples, we examine the Chen system and Liu system, demonstrating how these numerical cases support our theoretical findings.