Hello Austin,
I understand that you want to solve a system (Ax=b) using the Jacobi method and calculating the infinity norm of (|t-x^i|).
Here's a corrected version of your script with comments:
A = [4 -1 -1 0;-1 4 0 -1;-1 0 4 -1;0 -1 -1 4]';
b = [10.5;-13;1;-1.5];
n = 4;
%% exact solution
t = [2;-3;0.5;-1];
x0 = [0; 0; 0; 0];
%% Initialize x for infinity norm calculation
x = x0;
%% Print header for the table
fprintf('Iteration\tInfinity Norm\n');
for i = 1:20
x_new = Jacobi(A, b, x, n); % Get the new x using Jacobi method
z = norm(t - x_new, inf); % Calculating the infinity norm
% Print the current iteration and infinity norm
fprintf('%d\t\t\t%f\n', i, z);
x = x_new; % Update x for the next iteration
end
function x_new = Jacobi(A, b, x, n)
x_new = zeros(n, 1); % Initialize new x vector for the current iteration
for i = 1:n
sum = 0;
for j = 1:n
if j ~= i
sum = sum + A(i, j) * x(j);
end
end
x_new(i) = (b(i) - sum) / A(i, i);
end
end
This script now correctly performs 20 iterations of the Jacobi method to solve the system (Ax=b) and prints the infinity norm of (|t-x^i|) after each iteration.
Hope this helps,
Thanks,
Balaji
