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

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American Journal of Computational Mathematics 2023年第4期13卷 644-677页

作者： Isaac Azure Japheth Kodua Wiredu Anas Musah Eric Akolgo Department of Computer Science Regentropfen College of Applied Sciences Bolgatanga Ghana

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 comput

关键词： System of Nonlinear Equations broyden method Robustness Index Artificial Intelligence (AI) MATLAB SCILAB Python

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Efficient Numerical Scheme for the Solution of HIV Infection CD4^(+)T-Cells Using Haar Wavelet Technique

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Computer Modeling in Engineering & Sciences 2022年第5期130卷 639-653页

作者： Rohul Amin Suayip Yuzbasi Shah Nazir Department of Mathematics University of PeshawarPeshawar25120Pakistan Department of Mathematics Faculty of ScienceAkdeniz UniversityAntalyaTr-07058Turkey Department of Computer Science University of SwabiSwabi23430Pakistan

In this paper,Haar collocation algorithmis developed for the solution of first-order ofHIV infection CD4^(+)T-Cells *** this technique,the derivative in the nonlinear model is approximated by utilizing Haar *** value of the unknown function is obtained by the process of *** estimation is also discussed,which aims to reduce the error of numerical *** numerical results show that the method is simply *** results are compared with Runge-Kutta technique,Bessel collocation technique,LADM-Pade and Galerkin technique available in the *** results show that the Haar technique is easy,precise and effective.

关键词： System of nonlinear differential equations HIV infection of CD4^(+)T-cells broyden method Haar wavelet residual error estimation

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SVM-based Identification and Un-calibrated Visual Servoing for Micro-manipulation

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International Journal of Automation and computing 2010年第1期7卷 47-54页

作者： Xin-Han Huang Xiang-Jin Zeng Min Wang Department of Control Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, PRC Department of Control Science and Engineering Huazhong University of Science and Technology Wuhan PRC

This paper presents an improved support vector machine （SVM） algorithm, which employs invariant moments-based edge extraction to obtain feature attribute. A heuristic attribute reduction algorithm based on rough set＇s discernible matrix is proposed to identify and classify micro-targets. To avoid the complicated calibration for intrinsic parameters of camera, an improved broyden＇s method is proposed to estimate the image Jacobian matrix which employs Chebyshev polynomial to construct a cost function to approximate the optimization value. Finally, a visual controller is designed for a robotic micromanipulation system. The experiment results of micro-parts assembly show that the proposed methods and algorithms are effective and feasible.

关键词： Micro-assembly support vector machine part identification broyden method visual servoing

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Brown-broyden修正算法

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高等学校计算数学学报 2001年第4期23卷 368-377页

作者：王德人王新力上海大学数学系上海大学数学系上海201800

In this paper, we proposed Brown-broyden update algorithm for solving systems of nonlinear equations. We prove the local superlinear convergence of the proposed algorithm. Numerical experiments show the superiority of... 详细信息

关键词： systems of nonlinear equations Brown method broyden method local convergence.

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