8/22/2023 0 Comments All matrix gauss seidel pythonNow, if I used the Gauss-Seidel solution, this is what I get: x = Specifically, this system is diagonally dominant.Įxample #1 A = Where we specify a system that does converge by Jacobi.Where we specify a system that does not converge by Jacobi, but there is a solution.Here are two examples that I will show you: To make this Gauss-Seidel, all you have to do is change one character within your for loop. The only difference is that you are re-using the solution of x and feeding it into the other variables as you progress down the rows. It's actually more stable if you use Gauss-Seidel. However, there are some systems that will converge with Jacobi, even if this condition isn't satisfied, but you should use this as a general rule before trying to use Jacobi for your system. In other words, for each row i in your matrix, the absolute summation of all of the columns j at row i without the diagonal coefficient at i must be less than the diagonal itself. To be specific (thanks to this method will converge if your matrix A is strictly diagonally dominant. The reason why it may not seem to work is because you are specifying systems that may not converge when you are using Jacobi iterations.
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