Polinomio De Newton Rapson

Polinomio de Newton R=60

'(-0.033333)*(X - 0) + (-0.01)*(X - 0)*(X - 6) + (6.9444e-005)*(X - 0)*(X - 6)*(X - 12) + (-4.501e-006)*(X - 0)*(X - 6)*(X - 12)*(X - 18) + (6.43e-008)*(X - 0)*(X - 6)*(X - 12)*(X - 18)*(X - 24) + (1.1907e-009)*(X - 0)*(X - 6)*(X - 12)*(X - 18)*(X - 24)*(X - 30) + (-2.6225e-010)*(X - 0)*(X - 6)*(X - 12)*(X - 18)*(X - 24)*(X - 30)*(X - 36) + (1.6243e-011)*(X - 0)*(X -6)*(X - 12)*(X - 18)*(X - 24)*(X - 30)*(X - 36)*(X - 42) + (-9.434e-013)*(X - 0)*(X - 6)*(X - 12)*(X - 18)*(X - 24)*(X - 30)*(X - 36)*(X - 42)*(X - 48) + (-2.6889e-015)*(X - 0)*(X - 6)*(X - 12)*(X - 18)*(X - 24)*(X - 30)*(X - 36)*(X - 42)*(X - 48)*(X - 54) + 59.9'
Script
X=[0 6 12 18 24 30 36 42 48 54 60];
Y=[59.9 59.7 58.78 57.23 55 51.96 48 42.8 36 26.15 0.43];
n=length(X);
fdd=zeros(n);xint=5;
%llenando fdd con diferencias divididas
for i=1:n
fdd(i,1)=Y(i);
end

for i=2:1:n
for j=1:1:n+1-i
fdd(j,i)=(fdd(j+1,i-1)-fdd(j,i-1))/(X(i+j-1)-X(j));
end
end
Pol='';
Prod='';
for i=1:1:n-1
Prod='';
for j=1:1:i
Prod=[Prod,'(X - ',num2str(X(j)),')'];
end
Pol=[Pol,'(',num2str(fdd(1,i+1)),')',Prod,' + '];
end
Pol=['F(x) =',Pol,num2str(Y(1)),'\n\n'];

fprintf('Matriz de diferencias divididas:\n');
fdd
fprintf('Polinomio de Newton calculado:\n\n');
fprintf(Pol);

fint=0;
xprod=1;
sum=fdd(1,1);
for i=1:1:n-1
fint=fdd(1,i+1);
xprod=1;
for j=1:1:i
xprod=xprod*(xint-X(j));
end
fint=fint*xprod;
sum=sum+fint;
end
fint=sum;
%graficando el polinomio de newton
fint1=0;xprod1=1;
xn=1:0.01:max(X)+max(X)*0.25;
yn=[];
for k=1:1:length(xn)
sum1=fdd(1,1);
for i=1:1:n-1
fint1=fdd(1,i+1);
xprod1=1;
for j=1:1:i
xprod1=xprod1*(xn(k)-X(j));
end
fint1=fint1*xprod1;
sum1=sum1+fint1;
end
fint1=sum1;
yn(k)=fint1;
end

Error=abs((log(xint)-fint)/log(xint));

fprintf('Evaluando el polinomio en X = %f resulta: %f\n\n',xint,fint);xg=1:0.1:max(X)+max(X)*0.25;
yg=log(xg);
plot(xg,yg,'r')
hold on;
plot(X,Y,'bo');
hold on;
plot(xint,fint,'r+');
hold on;
plot(xn,yn,'b');
hold on;
plot(xint,log(xint),'ro');
hold off;
title('Representacion grafica de Ln(x) y el polinomio de Newton');
xlabel('X');
ylabel('Y = Ln(X)');
legend('Ln(x)','Puntos insertados','Valor interpolado','polinomio de Newton','valor real');
Vari=['X= ',num2str(xint),' Y = ',num2str(fint),' Er = ',num2str(Error),' Ea = ',num2str(Error*100),' %'];
text(xint+xint*.1,fint,Vari);

La compilación de Matriz de diferencias divididas nos entrega los siguientes resultados:
fdd =
Columns 1 through 7
59.9000 -0.0333 -0.0100 0.0001 -0.0000 0.0000 0.0000
59.7000 -0.1533 -0.0088 -0.0000 -0.0000 0.0000 -0.000058.7800 -0.2583 -0.0094 -0.0001 0.0000 -0.0000 0.0000
57.2300 -0.3717 -0.0113 -0.0001 -0.0000 0.0000 -0.0000
55.0000 -0.5067 -0.0128 -0.0002 -0.0000 -0.0000 -0.0000
51.9600 -0.6600 -0.0172 -0.0003 -0.0000 -0.0000 0
48.0000 -0.8667 -0.0222 -0.0011 -0.0004 0 0
42.8000 -1.1333 -0.0424 -0.00990 0 0
36.0000 -1.6417 -0.2204 0 0 0 0
26.1500 -4.2867 0 0 0 0 0
0.4300 0 0 0 0 0 0
Columns 8 through 11
-0.0000 0.0000 -0.0000 -0.0000
0.0000 -0.0000 -0.0000 0
-0.0000 -0.0000 0 0-0.0000 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0
0 0 0 0

Polinomio de Newton calculado:

F(x) = (-0.033333)(X - 0) +...