m=5;
A = toeplitz([1;-ones(m-1,1)],[1 zeros(1,m-1)]); A(:,m)=1
[L,U]=lu(A)
m=50;
A=[2 1 1 0; 4 3 3 1; 8 7 9 5; 6 7 9 8 ];
A = toeplitz([1;-ones(m-1,1)],[1 zeros(1,m-1)]); A(:,m)=1;
x = rand(50,1);
b = A*x;
[L,U]=lu(A);
x1 = U\(L\b);
norm(x-x1)/norm(x)
m=55;
A = toeplitz([1;-ones(m-1,1)],[1 zeros(1,m-1)]); A(:,m)=1;
[L,U]=lu(A);
x=[];
x = rand(50,1);
b = A*x;
x = rand(m,1);
b = A*x;
x1 = U\(L\b);
norm(x-x1)/norm(x)
cond(A)
[Q,R]=qr(A);
x2=R\(Q'*b);
norm(x-x2)/norm(x)
x3 = A\b;
norm(x-x3)/norm(x)
edit cholesky
A = rand(6,4)+1i*rand(6,4)
B=A'*A
R=cholesky(B)
R'*R - B
chol(B)
A=[2 1 1 0; 4 3 3 1; 8 7 9 5; 6 7 9 8 ]
A=A+A'
chol(A)