tablade diferencia divididas

%tablade diferencia divididas
x=[-1;0;1;2];
f=[-2,1,3,13];
n=length(x)-1;
for i=1:n
t(i,1)=(f(i+1)-f(i));
end
for j=2:n
for i=j:n
t(i,j)=((t(i,j-1)-t(i-1,j-1))/(x(i+1)-x(i-j+1)));
end
end
t

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lagrnange

%lagrnage
x=[-1;0;1;2];
y=[-2,1,3,13];
n=length(x)-1;
l=zeros(n+1,n+1);
for k=1:n+1
v=1;
for j=1:n+1
if k~=j
v=conv(v,poly(x(j)))/(x(k)-x(j));
end
end
l(k,:)=v;
end
l

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interpolacion polnomial

% interpolacion polinomial

x=[-1;0;1;2];
y=[-2;1;3;13];
n=length(x)-1;
b(:,n+1)=ones(size(x));
b(:,n)=x;

for k=n-1:-1:1
b(:,k)=b(:,k+1).*x;
end

b

a=inv(b)*y

%interpolacion

x0=[0.5;1.5];
y0=zeros(size(x0));

for k=1: n+1
y0=(y0+a(k)*x0.^(1+n-k)); k=1:n+1
end
y0

%grafica
xp=-1:0.01:2;
yp=zeros(size(xp));

for k=1:n+1
yp=(yp+a(k)*xp.^(1+n-k));

end

plot (xp,yp,x,y,'ob')
hold on
plot(x0,y0,'+r')

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