Scholarlink

<p>This study delves into the convergence analysis of Hansen-Patrick-like family of methods designed for resolution of non-linear equations within the framework of Riemannian Manifolds. Majority of methods within this family exhibit third-order convergence, with a notable exception: one method attains fourth-order convergence. To shed light on the unique properties of the fourth-order method, we have developed an algorithm for locating its singular points within the Riemannian Sphere <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(S^2\)</EquationSource> </InlineEquation>. Our investigation culminates in a comparative analysis, demonstrating the superior convergence performance of the fourth-order method when juxtaposed with the classical Newton and Euler-Chebyshev methods. This research underscores the potential of advanced numerical techniques in the realm of nonlinear equation solving on Riemannian Manifolds, offering valuable insights for both theoretical and practical applications.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Convergence analysis of Hansen-Patrick-like family in Riemannian manifold

  • 期刊论文

  • 发表日期：

    2026年4月30日

查看全文
  • Babita Mehta,
  • P. K. Parida

摘要

This study delves into the convergence analysis of Hansen-Patrick-like family of methods designed for resolution of non-linear equations within the framework of Riemannian Manifolds. Majority of methods within this family exhibit third-order convergence, with a notable exception: one method attains fourth-order convergence. To shed light on the unique properties of the fourth-order method, we have developed an algorithm for locating its singular points within the Riemannian Sphere \(S^2\) . Our investigation culminates in a comparative analysis, demonstrating the superior convergence performance of the fourth-order method when juxtaposed with the classical Newton and Euler-Chebyshev methods. This research underscores the potential of advanced numerical techniques in the realm of nonlinear equation solving on Riemannian Manifolds, offering valuable insights for both theoretical and practical applications.