I'm solving a system Ax=b with Jacobi. I got it to run through once, but now I need a driver to run 20 iterations of each, while printing the infinity norm of ||t-x^i|| ,where x^i is generated from an initial guess of x0, to a table each iteration.

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Austin Marsh 2021-3-4

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https://ww2.mathworks.cn/matlabcentral/answers/762906-i-m-solving-a-system-ax-b-with-jacobi-i-got-it-to-run-through-once-but-now-i-need-a-driver-to-run

回答： Balaji 2024-5-15

function driver

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;.5;-1];

x0=[0; 0; 0; 0];

%% updated x vector for infinity norm

x=(1:n);

for i= 1:20

if i = 1

%% initiating jacobi with x0

x = x0;

else x=x(i);

end

Jacobi(A,b,x,n)

%% calculating the infinity norm each iteration

z=norm(t-x(i),inf);

end

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Answer 1

Balaji 2024-5-15

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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