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]

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poppy 2022-11-27

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回答： Ishan 2022-11-29

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]?

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Answer 1

Ishan 2022-11-29

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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