![]() ![]() Small modifications in your algorithm can yield different results. We will in this section seek to illustrate how classical iterative methods for linear algebraic systems of equations, such as Jacobi, Gauss-Seidel or SOR, may be applied for the numerical solution of linear, elliptical PDEs, whereas criteria for convergence of such iterative schemes can be seen in Section 7.3.2 of the Numeriske Beregninger. 235 12K views 2 years ago Numerical Analysis Course The Gauss-Seidel Method is an iterative numerical method that can be used to easily solve non-singular linear matrices. (Jacobi and Gauss-Seidel methods) Write a python code for solving a system of linear equations by Jacobi method and Gauss-Seidel method. We can see, that for a value of $\omega\approx 0.38$ we get optimal convergence.Įven though this might be a little more than you asked for, I still hope it might interest you to see, that &3 & 1 & -2 \end-x$ for different values of $\omega$ on the x-axis, once for $0.01<\omega<2$ and in the second plotįor $0.01<\omega<0.5$. ![]() ![]() With the spectral radius, you are on the right track. ![]()
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