An Algorithm on the Numerical Continuation of Asymmetric and Symmetric Periodic Orbits Based on the Broyden’s Method and Its Application

Xu, Xingbo

doi:10.1016/j.chinastron.2022.11.010

Cited by 1 publication

(1 citation statement)

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“…It does so by updating an initial approximation of the Jacobian matrix using information from previous iterations. This update makes the method more efficient and less computationally demanding than Newton's method [17].…”

Section: The Broyden Methodsmentioning

confidence: 99%

AI-Enhanced Performance Evaluation of Python, MATLAB, and Scilab for Solving Nonlinear Systems of Equations: A Comparative Study Using the Broyden Method

Azure,

Wiredu,

Musah

et al. 2023

AJCM

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This research extensively evaluates three leading mathematical software packages: Python, MATLAB, and Scilab, in the context of solving nonlinear systems of equations with five unknown variables. The study's core objectives include comparing software performance using standardized benchmarks, employing key performance metrics for quantitative assessment, and examining the influence of varying hardware specifications on software efficiency across HP ProBook, HP EliteBook, Dell Inspiron, and Dell Latitude laptops. Results from this investigation reveal insights into the capabilities of these software tools in diverse computing environments. On the HP ProBook, Python consistently outperforms MATLAB in terms of computational time. Python also exhibits a lower robustness index for problems 3 and 5 but matches or surpasses MATLAB for problem 1, for some initial guess values. In contrast, on the HP EliteBook, MATLAB consistently exhibits shorter computational times than Python across all benchmark problems. However, Python maintains a lower robustness index for most problems, except for problem 3, where MATLAB performs better. A notable challenge is Python's failure to converge for problem 4 with certain initial guess values, while MATLAB succeeds in producing results. Analysis on the Dell Inspiron reveals a split in strengths. Python demonstrates superior computational efficiency for some problems, while MATLAB excels in handling others. This pattern extends to the robustness index, with Python showing lower values for some problems, and MATLAB achieving the lowest indices for other problems. In conclusion, this research offers valuable insights into the comparative performance of Python, MATLAB, and Scilab in solving nonlinear systems of equations. It underscores the importance of considering both software and hardware specifica-How to cite this paper: Azure, I., Wiredu,

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Section: The Broyden Methodsmentioning

confidence: 99%