%% Part 1: Crout factorization
n=10 A = full(gallery('tridiag',n,-1,2,-1)) i = 2:(n-1); bmid = i.^2 / ((n+1).^4) b = [1+1/(n+1)^4, bmid, 6+(n^2)/(n+1)^4]' for i = 1:n L(i,1) = A(i,1) end
for j = 1:n U(1,j) = A(1,j)/L(1,1) end
for j = 2:n for i = j:n sum = 0.0 for k = 1:(j-1) sum = sum + L(i,k) * U(k,j) end L(i,j) = A(i,j) - sum end
U(j,j) = 1;
for i = (j+1):n
sum = 0.0
for k = 1:(j-1)
sum = sum + L(j,k) * U(k,i)
end
U(j,i) = (A(j,i) - sum)/L(j,j)
end
end
x=A\b
error=max(abs(b-A*x))
%% Part 2: Gauss Seidel iteration n = 10 n = 10 A = 2*diag(ones(n,1)) - diag(ones(n-1,1),-1) - diag(ones(n-1,1),1); L = 2*diag(ones(n,1)) - diag(ones(n-1,1),-1); U = -diag(ones(n-1,1),1);
b = 1/(n+1)^4*(1:n)'.^2
b(1) = b(1) + 1; b(n) = b(n) + 6
x = zeros(n,1)
X = ones(n,1)
tol = 10e-8;
epsilon = 10*tol
while (epsilon > tol)
x = inv(L)*(b-U*x)
epsilon = max(abs(X-x))
X = x;
end
Can someone tell me are these algorithms correct or not because when I try to perform 1000x1000 matrix, it is taking me more than a hour to compute the result.
