Question

Matlab code for Gauss Siedel with solved example in Matlab

Answer 1

% Gauss-Seidel Method in MATLAB

function x = gauss_siedel( A ,B )
disp ( 'Enter the system of linear equations in the form of AX=B')

%Inputting matrix A

A = input ( 'Enter matrix A : \n')
% check if the entered matrix is a square matrix

[na , ma ] = size (A);
if na ~= ma
disp('ERROR: Matrix A must be a square matrix')
return
end

% Inputting matrix B

B = input ( 'Enter matrix B : ')
% check if B is a column matrix

[nb , mb ] = size (B);
if nb ~= na || mb~=1
disp( 'ERROR: Matrix B must be a column matrix')
return
end

% Separation of matrix A into lower triangular and upper triangular matrices

% A = D + L + U

D = diag(diag(A));
L = tril(A)- D;
U = triu(A)- D

% check for convergence condition for Gauss-Seidel method

e= max(eig(-inv(D+L)*(U)));
if abs(e) >= 1
disp ('Since the modulus of the largest Eigenvalue of iterative matrix is not less than 1')
disp ('this process is not convergent.')
return
end

% initial guess for X..?

% default guess is [ 1 1 .... 1]

r = input ( 'Any initial guess for X? (y/n): ','s');
switch r
case 'y'
% asking for initial guess
X0 = input('Enter initial guess for X :\n')
% check for initial guess
[nx, mx] = size(X0);
if nx ~= na || mx ~= 1
disp( 'ERROR: Check input')
return
end
otherwise
X0 = ones(na,1);
end

% allowable error in the final answer

t = input ( 'Enter the error allowed in final answer: ');
tol = t*ones(na,1);
k= 1;

X( : , 1 ) = X0;
err= 1000000000*rand(na,1);% initial error assumption for looping
while sum(abs(err) >= tol) ~= zeros(na,1)
X ( : ,k+ 1 ) = -inv(D+L)*(U)*X( : ,k) + inv(D+L)*B;% Gauss-Seidel formula
err = X( :,k+1) - X( :, k);% finding error
k = k + 1;
  
end

fprintf ('The final answer obtained after %g iterations is \n', k)
X( : ,k)