In both cases, x is the final solution vector and i returns the number of iterations.
I have created the below code for each of them, however my final solution vector does not return the correct answers and i'm really struggling to figure out why. This code was originally written for Jacobi, and I provided the modification for making it into Gauss-Seidel.I need to code the Gauss Seidel and Successive over relaxation iterative methods in Matlab. 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.
The Matlab code runs in 20 s whereas the Numpy codes takes 30 s. The code was originally written in MATLAB and then transferred to Python. Y(idx) = C(idx,1:idx-1)*y(1:idx-1) + C(idx,idx:end)*x(idx:end) + D(idx) I currently have a Gauss-Seidel solver implemented in both MATLAB and Numpy which acts on a 2D axisymmetric domain (cylindrical coordinates). If idx = 1 %// Case where we are solving for the first variable Expressed mathematically, x x1, x2., xnT xL max xi i 1, 2., n An example using an iterative method Consider the system: E1: 10x1 x2 + 2x3 6 E2: x1 + 11x2 x3 + 3x4 25 E3: 2x1 x2 + 10x3 x4 11 E4: 3x2 x3 + 8x4 15 Let us solve each equation, Ej, for the variable xj. 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. matrix linear-algebra gaussian numerical-methods gauss-elimination jacobian newton-raphson secant gauss-jordan jacobi-iteration gauss-jordan-elimination secant-method newton-raphson-algorithm. For Jacobi, you are simply using the previous iteration's solution to formulate the current solution. All of the code written in C++ with five methods included. , x_) as part of the solution for the current variable x_i.
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.
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