solve the linear system of equations using gauss-seidel iteration solver in matlab

The Gauss-Seidel method is an iterative technique used to solve linear systems of equations. In MATLAB, we can use the gauss_seidel function from the Optimization Toolbox to solve these systems.

Here is an example code that shows how to use the gauss_seidel function to solve the linear system of equations:

main.m
% define the system of equations in matrix form
A = [4 -1 0; 1 3 -1; 0 -1 4];
b = [7; 6; 8];

% initial guess for the solution
x0 = [1; 1; 1];

% maximum number of iterations
max_iter = 1000;

% convergence tolerance
tol = 1e-6;

% use the gauss_seidel function to solve the system
x = gauss_seidel(A, b, x0, max_iter, tol)
324 chars
16 lines

In the code above, we first define the system of equations as a matrix A and a vector b. We also define an initial guess for the solution x0.

Next, we set the maximum number of iterations and the convergence tolerance. The gauss_seidel function will continue iterating until either the maximum number of iterations is reached or the error between successive iterates falls below the tolerance level.

Finally, we call the gauss_seidel function with the inputs A, b, x0, max_iter, and tol to solve the system of equations. The function returns the solution vector x.