This code was originally written for Jacobi, and I provided the modification for making it into Gauss-Seidel. Above is my Gauss-Seidel method in Python. If you want, there is another way to calculate Jacobi and Gauss-Seidel, and you can take a look at that post here: Jacobi iteration doesn't end. Once we pass this point, then we use the variables calculated from the current iteration from the first variable up to the point where we are calculating, then use the rest of the variables for calculating the solution.

If we are working on calculating the first variable, then we don't have any new information yet, and so we simply just update the solution using all of the previous information from the previous iteration. python - Improving Numpy speed for Gauss-Seidel (Jacobi) Solver - Stack Overflow Improving Numpy speed for Gauss-Seidel (Jacobi) Solver Ask Question Asked 10 years ago Modified 10 years ago Viewed 6k times 3 This question is a follow-up to a recent question posted regarding MATLAB being twice as fast as Numpy. Due to the fewer number of iterations, the absolute time to solution is. If idx = 1 %// Case where we are solving for the first variable Gauss-Seidel, like our two Jacobi implementations, appears to be an O(n2) algorithm. Therefore: function z=gaussseidel(A,B) %// Change the function name This has to be done in the while loop, because that's where you're doing the iterations. For Gauss-Seidel, for each variable that you solve for, you must use the solutions of the previous variables calculated from the current iteration as part of the solution for the variable you are focusing on.Īs such, for your particular version of the code (though not optimal.), you simply need to add in a for loop where we solve for each variable one at a time, then keep feeding this information into the other variables. For Jacobi, you are simply using the previous iteration's solution to formulate the current solution. , x_) as part of the solution for the current variable x_i. The G-S use the updated values computed in the loop just before and take twice less time to solve the problem than Jacobi (Jacobi don't use updated values).The difference between a Jacobi solver and a Gauss-Seidel solver is that when you're solving for the solution of a variable x_i at the current iteration, you need to use the information from the previous variables ( x_1, x_2. It works using loop but loops are slow (~1s per iteration), so I tried to vectorize the expression and now the G-S (thus SOR) don't work anymore.

I did the Jacobi, Gauss-seidel and the SOR using Numpy.

I wrote a code to solve a heat transfer equation (Laplace) with an iterative method.

Python gauss seidel