1> A = [1 1+0.5e-15 3; 2 2 20; 3 6 4]
A =

    1.0000    1.0000    3.0000
    2.0000    2.0000   20.0000
    3.0000    6.0000    4.0000



2> 


2> [l, u, p] = lu(A)
l =

   1.00000   0.00000   0.00000
   0.66667   1.00000   0.00000
   0.33333   0.50000   1.00000

u =

    3.00000    6.00000    4.00000
    0.00000   -2.00000   17.33333
    0.00000    0.00000   -7.00000

p =

Permutation Matrix

   0   0   1
   0   1   0
   1   0   0



3> p * A - l * u
ans =

   0   0   0
   0   0   0
   0   0   0



4> hilb(4)
ans =

   1.00000   0.50000   0.33333   0.25000
   0.50000   0.33333   0.25000   0.20000
   0.33333   0.25000   0.20000   0.16667
   0.25000   0.20000   0.16667   0.14286



5> help sol
`sol' is a function from the file C:\Documents and Settings\rudiger.achilles\desktop\sol.m

SOL(A,b) Trova la soluzione di un sistema lineare 
   A*x = b utilizzando la fattorizzazione di Gauss 
   con pivoting per righe.

Additional help for built-in functions and operators is
available in the on-line version of the manual.  Use the command
`doc <topic>' to search the manual index.

Help and information about Octave is also available on the WWW
at http://www.octave.org and via the help@octave.org
mailing list.


6> clear A


7> A = hilb(13);


8> x = ones(13,1);


9> b = A * x
b =

   3.18013
   2.25156
   1.81823
   1.54740
   1.35622
   1.21177
   1.09774
   1.00488
   0.92750
   0.86184
   0.80532
   0.75608
   0.71275



10> x_calc = sol(A,b)
x_calc =

   1.00000
   0.99999
   1.00037
   0.99400
   1.05308
   0.71559
   1.98219
  -1.25796
   4.49045
  -2.58490
   3.34539
   0.11545
   1.14635



11> err_rel = norm(x - x_calc)/norm(x)
err_rel =  1.6981


12>  % errore percentuale


12> err_rel * 100
ans =  169.81


13> sqrt(13)
ans =  3.6056


14> norm(x)
ans =  3.6056


15> clear x


16> x = linspace(-1,10);


17> y = 2 * exp(3*x);


18> plot(x,y)


19> semilogy(x,y)


20> for n = 1 : 100
> A = hilb(n); x = ones(n,1); b = A * x;
> x_calc = sol(A,b); 
> err_rel(n) = norm(x - x_calc)/norm(x);
> [l, u, p] = lu(A); 
> r(n) =  max(max(abs(l*u - p*A)));
> end;


21> size(err_rel)
ans =

     1   100



22> semilogy(1:100,err_rel,1:100,r,'r')


23> grid on


24> cond(5)
ans =  1


25> cond(hilb(5))
ans = 4.7661e+005


26> cond(hilb(1))
ans =  1


27> cond(hilb(2))
ans =  19.281


28> cond(hilb(100))
ans = 1.4641e+019


29> quit