% Starting diary file diary-20-Oct-2010.txt

A = 4
b = 1
xstar = A \ b
x = .2
error = x - xstar
residual = A*x - b
A * error
residual

A = [ 2 -1 ; -1 2]
b = [0 ; 3]
A \ b
xstar = [ 1 ; 2]
A * xstar - b
x = [1.1 ; 2.2]
error = x - xstar
residual = A * x - b

v = [1;2;3]
norm(v)
1 + 4 + 9
sqrt(14)

norm(v,2)
norm(v,3)
norm(v,1)
norm(v,Inf)
norm(v)

error
residual
norm(error)
norm(residual)

A
x = [1;1]
A*x
norm(x)
norm(A*x)
norm(A*x) / norm(x)

x = [ 1 ; -1 ]
norm(x)
A * x
norm(A*x)
norm(A*x) / norm(x)

for i = 1:100
x = randn(2,1);
stretch(i) = norm(A*x) / norm(x);
end;

plot(stretch,'.')
hist(stretch)
min(stretch)
max(stretch)
eigshow(A)
norm(A)

clc
A1 = A
A2 = [1.6 1.5 ; 1.5 1.4]
norm(A1)
norm(A2)
x = [ 1 ; 1]
A2*x
norm(A2*x)/norm(x)
x = [ 1 ; -1 ]
norm(x)
A2*x
norm(A2*x)/norm(x)

eigshow(A1)
eigshow(A2)

cond(A1)
cond(A2)

A = randn(1000);
cond(A)
tic, cond(A), toc
tic,lu(A);toc
load temperature
size(A100)
help condest
cond(A)
condest(A)

size(A100)
cond(A1)
cond(A2)
condest(A100)
t = A100\b100;
resid = norm(A100*t-b100)

diary off