How can I make a guess sidel function with the given variables: GS(Am,bm,i​nitial_gue​ss,10^-4) and the range is 𝑁 = [20, 40, 80, 160, 320, 640, 1280]

How can I make a guess sidel function with the given variables: GS(Am,bm,initial_guess,10^-4) and the range is 𝑁 = [20, 40, 80, 160, 320, 640, 1280]?

Answer 1

[Ishan]

Hi Anujan,

If you want to solve a linear equation by Gauss-Seidel method, you can use the below function to do so:

%A = input('Enter a Co-effecient Matrix A: ');
A = [10 3 1;3 10 2;1 2 10];
%B = input('Enter Source Vector B: ');
B = [19;29;35];
%P = input('Enter initial Guess Vector: ');
P = [0;0;0];
%n = input('Enter no. of iterations: ');
n = 10;
%e = input('Enter your tollerance: ');
e = 0.0001

e = 1.0000e-04

N = length(B);
X = zeros(N,1);
Y = zeros(N,1);

for j=1:n
    for i = 1:N
        X(i) = (B(i)/A(i,i))-(A(i,[1:i-1,i+1:N])*P([1:i-1,i+1:N]))/A(i,i);
        P(i) = X(i);
    end
fprintf('Iteration no. %d\n', j)
X
if abs(Y-X)<e
    break
end
Y=X;
end

Iteration no. 1

X = 3×1

1.9000 2.3300 2.8440

Iteration no. 2

X = 3×1

0.9166 2.0562 2.9971

Iteration no. 3

X = 3×1

0.9834 2.0056 3.0005

Iteration no. 4

X = 3×1

0.9983 2.0004 3.0001

Iteration no. 5

X = 3×1

0.9999 2.0000 3.0000

Iteration no. 6

X = 3×1

1.0000 2.0000 3.0000

Iteration no. 7

X = 3×1

1.0000 2.0000 3.0000

Hope this helps you solve your problem!