35 lines
716 B
Matlab
35 lines
716 B
Matlab
function [L, U] = Alg7(A)
|
|
% LU Factorization without pivoting
|
|
% [L, U] = Alg7(A) decomposes matrix A using Crout's algorithm into
|
|
% U - upper triangular matrix and L - unit lower triangular matrix
|
|
% such that A = LU.
|
|
|
|
[m, n] = size(A);
|
|
|
|
% This solution is mathematically correct, however computationaly
|
|
% inefficient.
|
|
%
|
|
% A = Alg1_outer_product_gaussian_elimination(A);
|
|
%
|
|
% U = triu(A);
|
|
% L = tril(A, -1) + eye(m);
|
|
|
|
% Instead, we should use the Crout's algorithm
|
|
|
|
L = zeros(m, n);
|
|
U = eye(m, n);
|
|
|
|
for k = 1:n
|
|
|
|
for j = k : n
|
|
U(k, j) = A(k, j) - dot(L(k, 1:k-1), U(1:k-1, j));
|
|
end
|
|
|
|
for i = k:n
|
|
L(i, k) = (A(i, k) - dot(L(i,1:k-1), U(1:k-1, k))) / U(k,k);
|
|
end
|
|
|
|
|
|
end
|
|
|
|
end |