TITLE:
AI-Enhanced Performance Evaluation of Python, MATLAB, and Scilab for Solving Nonlinear Systems of Equations: A Comparative Study Using the Broyden Method
AUTHORS:
Isaac Azure, Japheth Kodua Wiredu, Anas Musah, Eric Akolgo
KEYWORDS:
System of Nonlinear Equations, Broyden Method, Robustness Index, Artificial Intelligence (AI), MATLAB, SCILAB, Python
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.13 No.4,
December
28,
2023
ABSTRACT: 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 specifications in real-world
applications. The choice between Python and MATLAB can yield distinct
advantages depending on the specific problem and computational environment,
providing guidance for researchers and practitioners in selecting tools for their unique challenges.