1> f = @(x) 1./(1 + x.^2);


2> x = linspace(-5,5);


3> plot(x, y)
error: 'y' undefined near line 3 column 9
error: evaluating argument list element number 2


3> plot(x, f(x))


4> nodic = -cos(pi/9*[0:9]) * 5
nodic =

  -5.00000  -4.69846  -3.83022  -2.50000  -0.86824   0.86824   2.50000   3.83022   4.69846   5.00000



5> p9c = polyfit(nodic, f(nodic), 9)
p9c =

 Columns 1 through 9:

  -1.2698e-020  8.3649e-006  5.3091e-019  -5.8345e-004  -6.1653e-018  1.4634e-002  6.2987e-018  -1.5759e-001  5.8390e-017

 Column 10:

  6.8090e-001



6> hold on


7> yp9c = polyval(p9c, x);


8> plot(x, yp9c, 'r')


9> nodic = -cos(pi/10*[0:10]) * 5;


10> p10c = polyfit(nodic, f(nodic), 10);


11> yp10c = polyval(p10c, x);


12> plot(x, yp10c, 'g')


13> errore = max(abs(f(x)-yp10c))
errore =  0.13185


14> x=linspace(-5,5,1.e6);


15> yp10c = polyval(p10c, x);


16> errore = max(abs(f(x)-yp10c))
errore =  0.13220


17> % Esempio di un'interpolazione instabile: 


17> % Quarteroni-Saleri, esempio 3.3, pag. 85


17> f=inline('sin(2*pi*x)')
f = f(x) = sin(2*pi*x)


18> nodi=linspace(-1,1,22);


19> p21=polyfit(nodi,f(nodi),21);


20> x=-1 : 0.01 : 1;


21> length(x)
ans =  201


22> % plottiamo la f (curva blu) e il polinomio interpolante (curva rossa);


22> % la curva rossa copre perfettamente la curva blue.


22> plot(x,f(x), x,polyval(p21,x),'r')


23> hold off


24> plot(x,f(x), x,polyval(p21,x),'r')


25> % numeri casuali normalmente distribuiti con la media 0


25> % e la deviazione standard 1


25> randn(1)
ans = -0.32536


26> randn(1)
ans =  0.56189


27> randn(1)
ans = -0.47643


28> randn(1)
ans =  0.16452


29> randn(1)
ans =  0.084893


30> randn(1)
ans = -1.1103


31> p21perturb = polyfit(nodi,f(nodi)+1.e-5*randn(1,22),21);


32> hold on


33> plot(x,polyval(p21perturb,x),'g')


34> p21perturb = polyfit(nodi,f(nodi)+1.e-4*randn(1,22),21);


35> plot(x,polyval(p21perturb,x),'k')


36> % costante di Lebesgue (stima)


36> 2^22/(exp(1)*21*(log(21)+0.57722))
ans = 2.0288e+004


37> quit