关键词: PyQt5, Python, 线性方程组, Jacobi迭代法, Gauss-Seidel迭代法, 幂法

Abstract: Aiming at the problem that high-dimensional linear equations are difficult and time-consuming to solve manually，this paper designed a linear equation-solving software based on PyQt5. This software solved linear equations input by users efficiently and in real-time based on Jacobi iteration and Gauss-Seidel iteration，judged the convergence of iterative methods using the power method，and visualized the iterative solution results. The text control was used to display the iterative results of the two iterative methods. The graph control was used to dynamically draw the graph of the error value obtained by the two iterative methods changing with the number of iterations and the graph of each independent variable value changing with the number of iterations. The overall interface design of this software was implemented in Qt Designer，and the partial interface display was dynamically generated by Python code according to user operations. The interface logic function was developed by Python's development tool PyCharm，using Python to write iterative algorithm code，call the PyQt5 library，and operate the interface. This software can intuitively compare the two iterative methods' convergence and quickly obtain the approximate solution value of the linear equation system. It has good real-time performance，a simple and beautiful interface，user-friendly operation，and has certain practical value.

Key words: PyQt5, Python, linear equations, Jacobi iteration, Gauss-Seidel iteration, power method