% Matlab diary from cs110a class #8, Jan 21 2005.
%
% This is what I typed in class.  
%
% Type it into Matlab yourself to
% reproduce the output I showed.

A = golub(7)
x = ones(7,1)
b = A*x
xstar = A \ b
e = x - xstar
norm(e)
r = b - A*xstar
norm(r)
help cond
I = eye(5)
cond(I)
B = 3*I
cond(B)
B = [1 0 0 ; 0 2 0; 0 0 3]
cond(B)
B * [0;0;1]
B*[1;0;0]
A
cond(A)
norm(r)
norm(e)
y = rand(7,1)
norm(y)
A*y
norm(A*y)
norm(A*y) / norm(y)
x
b = A*x
x = x+eps
x-ones(7,1)
x
newx = x
newb = A * newx
b
b - newb
deltax = newx - x
x
x = ones(7,1)
deltax = newx - x
deltab = A*newx - A*x
norm(deltax) / norm(x)
norm(deltab) /norm(b)
cond(A)
norm(A)
norm(inv(A))
norm(A) * norm(inv(A))
cond(A)
cond(A)
condest(A)
A = rand(5)
A = A + 5*eye(5)
A = A + A'
A - A'
R = chol(A)
U = R
L = R'
L*U
ans - A
(R') * R - A