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This article proposes a homotopy method to solve an electric network. This homotopy method works hand in hand with the Gauss–Seidel method to generate trajectories that converge to the solution of the electric network system at its via point while forming a loop within an interval of the homotopy parameter as iterations continue. Finally, this method is compared to the accelerated Gauss–Seidel method, significantly reducing the total number of iterations and obtaining more information from an iteration. Finally, conclusions and suggest possible future work are discussed.

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Enhancing Electric Network Solutions: A Comparative Study of Homotopy and Accelerated Gauss–Seidel Methods

  • 章节

  • 发表日期：

    2025年

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  • Yadira Quiñonez,
  • Oscar Zatarain,
  • Carmen Lizarraga,
  • Raquel Aguayo,
  • Juan C. Elizondo-Leal

摘要

This article proposes a homotopy method to solve an electric network. This homotopy method works hand in hand with the Gauss–Seidel method to generate trajectories that converge to the solution of the electric network system at its via point while forming a loop within an interval of the homotopy parameter as iterations continue. Finally, this method is compared to the accelerated Gauss–Seidel method, significantly reducing the total number of iterations and obtaining more information from an iteration. Finally, conclusions and suggest possible future work are discussed.