For Ax=b, How do I make LU decomposition (A=L*U) without using lu function. For example, A is nxn matrix and bis nx1 matrix.

clc
clear
A=rand(5)
b=rand(5,1);

A(2:3,1)
n=length(A)
U=A;
for i=1:n
    k=i+1
    i
    U(k:n,i)=U(k:n,i)-U(i,i)*(U(k:n,i)/U(i,i))
  
end
for k= 1:n
    L(k+1:n,k)=A(k+1:n,k)/A(k,k)
end

This is what I have try so far, I am very new to MATLAB like 2 week and genuinely struggle here.

Answer 1

[David Hill]

function [L,U] = mylu(A)
n = size(A,1);
for k = 1:n
    if A(k,k)==0
        warning('LU factorization fails');
        L = []; U = []; return; 
    end
    i = k+1:n;
    A(i,k) = A(i,k)/A(k,k);
    A(i,i) = A(i,i)-A(i,k)*A(k,i);
end
L = tril(A,-1)+eye(n); U = triu(A);