Gauss-Seidel Method in MATLAB

Question

Eric 2013-9-1

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/86085-gauss-seidel-method-in-matlab

回答： Harshad 2024-11-11

I have to write two separate codes for the Jacobi method and Gauss-Seidel

The question exactly is: "Write a computer program to perform jacobi iteration for the system of equations given. Use x1=x2=x3=0 as the starting solution. The program should prompt the user to input the convergence criteria value, number of equations and the max number of iterations allowed and should output the solution along with the number of iterations it took for the solution to convergence to the user specified value."

Gauss-Seidel:

%*************************Eric Douglas*****************************%
%***********************August 30th, 2013**************************%
%This code is used to compute the Jacobi Method of a certain matrix.%
%Input:
%       C_n = convergence criteria value
%       N = number of equations in the matrix
%       Imax = the maximum number of iterations
%Output:
%       S = the solution( M x 1 matrix ; jacobi approximation)
%       j = the number of iterations it took to
%           converge to the user inputed value
%       R = Residual Values
%establishes the variables needed
%B is an M x 1 matrix
%A is an M x M matrix
%P is the initial M x 1 matrix
%Z = remembering matrix
%Ask the user for each input statement required
Imax = input('What do you want the maximum iteration to be? ');
N = input('How many equations do you want? ');
C_n = input('What number do you want to converge to? ');
%Assigns the values inputed by the user into the matrices
for x=1:1:N
    for y=1:1:N
        strA = ['What do you desire your numbers in the matrix to be? ' num2str(x) 'Row: ' num2str(y) 'Column: '];
        A = input(strA);
    end
end
for l=1:1:N
    strB = ('What do you desire the Solution matrix to be? ');
    B = input(strB);
end
n = length(B);
X = zeros(n,1);
e = ones(n,1);
%%Check if the matrix A is diagonally dominant
for i = 1:n
    j = 1:n;
    j(i) = [];
    C = abs(A(i,j));
    Check(i,1) = abs(A(i,i)) - sum(B); % Is the diagonal value greater than the remaining row values combined?
    if Check(i) < 0
        fprintf('The matrix is not strictly diagonally dominant at row %2i\n\n',i)
    end
end

Main function for Gauss-Seidel

iteration = 0;
while max(e) > C_n%check error
    iteration = iteration + 1;
    Z = X;  % save current values to calculate error later
    for i = 1:N
        j = 1:N; % define an array of the coefficients' elements
        j(i) = [];  % eliminate the unknow's coefficient from the remaining coefficients
        Xtemp = X;  % copy the unknows to a new variable
        Xtemp(i) = [];  % eliminate the unknown under question from the set of values
        X(i,1) = (B(i,1) - sum(A(i,j) * Xtemp)) / A(i,i);
    end
    Xs = X;
    e = sqrt((X - Z).^2);
end
%%Display Results
Xs
iteration

There is an error at the line ("X(i,1) = (B(i,1) - sum(A(i,j) * Xtemp)) / A(i,i);") and it says "exceeds matrix index". I dont understand how to change this.

Also, if you see anything else wrong then I am open to comments/hints.

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Maria Clara Carvalho Rameiro 2018-2-21

移动：DGM 2024-10-29

I get the same error and I don't know how to fix it.

Imran Hossain 2021-3-13

Mathlab report question amader sikher jonno khub valo lage

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Answer 1

Walter Roberson 2013-9-1

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/86085-gauss-seidel-method-in-matlab#answer_95603

在 MATLAB Online 中打开

The line

A = input(strA);

overwrites all of A each time through the loop, so A is going to end up as a scalar.

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Answer 2

Muthu 2024-10-16

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/86085-gauss-seidel-method-in-matlab#answer_1532590

编辑：DGM 2024-10-29

在 MATLAB Online 中打开

% Define parameters for Gauss-Seidel method
maxIter = 100;  % Maximum number of iterations
tol = 1e-6;     % Tolerance for convergence
n = length(b);  % Number of equations
x = zeros(n, 1);  % Initial guess for the solution
for iter = 1:maxIter
    x_old = x;
    for i = 1:n
        sum1 = A(i, 1:i-1) * x(1:i-1);
        sum2 = A(i, i+1:end) * x_old(i+1:end);
        x(i) = (b(i) - sum1 - sum2) / A(i, i);
    end
    % Check for convergence
    if norm(x - x_old, inf) < tol
        break;
    end
end
% Display the results
disp('Solution for X, Y, Z using Gauss-Seidel method:');
disp(x);