How to solve a matrix using Cholesky Decompositon on Matlab

Question

I'm trying to solve a system of linear equations on MATLAB, I have written a code that solves the problem using Gaussian Elimination. But I was wondering how I could modify this to use other methods of matrix decomposition, such as Cholesky Decomposition?

%set up matrices
A=[-900 400 0 0 0; 500 -900 400 0 0; 0 500 -900 400 0; 0 0 500 -900 400; 0 0 0 400 -900];
b=[0;0;0;0;0];

%decompose A matrix
[L, U] = lu(A);

%set up series of yin's for plot
yin=0:0.01:0.25;
yout=zeros(length(yin),1);
xout=zeros(length(yin),1);

%create b based on yin, and solve
for i=1:1:length(yin)
 b(1)=-500*yin(i);
 d = L\b;
 y = U\d;
 %save yout and xout values before next iteration
 yout(i)=y(5);
 xout(i)=y(1)*4;
end

Answer 1

Given a self-adjoint positive-definite square matrix $A$, $\operatorname{chol}(A)$ returns an upper triangular matrix $U$ such that $A = U^* U$

To turn this into code, replace

[L, U] = lu(A);

by

U = chol(A);
L = U';