Small modifications in your algorithm can yield different results. 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 How to confirm if a system can be solved by Gauss-Seidel Ask Question Asked 6 years, 2 months ago Modified 6 years, 1 month ago Viewed 2k times 4 Given the system ( 5 1 2 2 5 2 1 3 3) ( x 3 x 1 x 2) ( 0 1 0) I have to say something concerning the convergence of Gauss-Seidel Method. &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 $0.01<\omega<0.5$.
Higher-dimensional discretizations 13.2.1. A solution to a system of linear equations is an x in Rn that satisfies the matrix form equation. Recall that this means there are m equations and n unknowns in our system. With the spectral radius, you are on the right track. We will further explain in more detail how to discretize partial differential equations in more than one dimension and introduce some of the simplest iterative solvers - the Jacobi and Gauss-Seidel iteration methods - to obtain the solution of the Poisson equation. Solutions to Systems of Linear Equations Consider a system of linear equations in matrix form, Ax y, where A is an m × n matrix.
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