LU decomposition Matlab
function LU = LUDecompDoolittle(A)
n = length(A);
LU = A;
% decomposition of matrix, Doolittle’s Method
for i = 1:1:n
for j = 1:(i - 1)
LU(i,j) = (LU(i,j) - LU(i,1:(j - 1))*LU(1:(j - 1),j)) / LU(j,j);
end
j = i:n;
LU(i,j) = LU(i,j) - LU(i,1:(i - 1))*LU(1:(i - 1),j);
end
%LU = L+U-I
end
function x = SolveLinearSystem(LU, B)
n = length(LU);
y = zeros(size(B));
% find solution of Ly = B
for i = 1:n
y(i,:) = B(i,:) - LU(i,1:i)*y(1:i,:);
end
% find solution of Ux = y
x = zeros(size(B));
for i = n:(-1):1
x(i,:) = (y(i,:) - LU(i,(i + 1):n)*x((i + 1):n,:))/LU(i, i);
end
end
A = [ 4 3 3; 6 3 3; 3 4 3 ]
LU = LUDecompDoolittle(A)
B = [ 1 2 3; 4 5 6; 7 8 9; 10 11 12 ]'
x = SolveLinearSystem(LU, B)
A * x