I am new to Matlab so details would be appreciated!
Please find posted the Matlab scripts gaussSeidel.m and gaussSeidelSolver.m. Run the script gaussSeidelSolver.m to test a case.
gaussSeidel.m
function x = gaussSeidel(A, b, tol)
% Gauss Siedel method
% x = gaussSiedel(A, b, tol)
% input:
% A = coefficient matrix
% b = right hand side vector
% tol = tolerance, stopping criterion
% output:
% x = solution vector
[nRows, nCols] = size(A);
% checks for Square Matrix
if nRows ~= nCols
error('Matrix must be square');
end
% checks for Diagonal Dominance
for m = 1: nRows
mthRow = abs(A(m, :));
d = sum(mthRow) - mthRow(m);
if mthRow(m) < d
error('Matrix is not
diagonally dominant');
end
end
% split Matrix into three matrices L, U, and D
D = diag(diag(A));
L = tril(A, 1);
U = triu(A, 1);
% sets Initial Guess
x0 = zeros(nRows, 1);
x = x0;
% starts the Iterative Method
iter = 0;
err = inf;
errVector = inf;
while err > tol
disp([num2str(iter) ' iteration,' ' x = '
mat2str(x) ', error = ' mat2str(errVector) '.']);
% update [x]
x_old = x;
x = inv(L + D) * (-U*x + b);
dx = x - x_old;
% error vector
errVector = abs(dx./x);
% estimate error
err = max(abs(dx./x));
iter = iter + 1;
end
% displays Result
disp(['Gauss Seidel method converges after ' num2str(iter) '
iterations.' ' x = ' mat2str(x) ' error = ' mat2str(errVector)
'.']);
end
gaussSeidelSolver.m
clear; clc;
A = [ -7 1 5;
0 -7 4;
1 2 -4];
b = [ -3 7 10 ]';
tol = 1e-3;
x = gaussSeidel(A, b, tol);
I am new to Matlab so details would be appreciated! Use Matlab or any other Language...
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