function [a,b,c,d]=spline3(X)%Pasos bsicos del algoritmo
obtenidos del libro Anlisis Numrico de%Richard Burden, 2a. Edicin,
Grupo Editorial Iberoamrica.n=length(X(1,:));for i=1:n;
a(i)=X(2,i);endfor i=1:n-1; h(i)=X(1,i+1)-X(1,i);endfor i=2:n-1;
alfa(i)=3/h(i)*(a(i+1)-a(i))-3/h(i-1)*(a(i)-a(i-1));endl(1)=1;mu(1)=0;z(1)=0;for
i=2:n-1; l(i)=2*(X(1,i+1)-X(1,i-1))-h(i-1)*mu(i-1);
mu(i)=h(i)/l(i);
z(i)=(alfa(i)-h(i-1)*z(i-1))/l(i);endl(n)=1;z(n)=0;c(n)=0;for
i=n-1:-1:1; c(i)=z(i)-mu(i)*c(i+1);
b(i)=(a(i+1)-a(i))/h(i)-h(i)*(c(i+1)+2*c(i))/3;
d(i)=(c(i+1)-c(i))/(3*h(i));endfor i=1:n-1; x=X(1,i):0.1:X(1,i+1);
y=a(i)+b(i)*(x-X(1,i))+c(i)*(x-X(1,i)).^2+d(i)*(x-X(1,i)).^3; hold
on; plot(x,y,'b');endfor i=1:n; hold on; plot
(X(1,i),X(2,i),'*','MarkerEdgeColor','r','LineWidth',1);
title('Interpolacin por "splines" de orden 3.');endPor ejemplo,
para los datos
{(1,0),(2,3),(3,4),(4,-6),(5,2),(6,4),(7,0),(8,4),(9,3)}, se
escribe en elCommand Window:>>X=[1 2 3 4 5 6 7 8 9; 0 3 4 -6
2 4 0 4 3];>>[m,b]=spline3(X)Y el programa entrega los
resultados:a = 0 3 4 -6 2 4 0 4 3b = 2.3806 4.2388 -7.3357 -1.8960
8.9196 -3.7826 0.2107 2.9398c = 0 1.8582 -13.4326 18.8723 -8.0567
-4.6455 8.6388 -5.9097 0d = 0.6194 -5.0969 10.7683 -8.9763 1.1371
4.4281 -4.8495 1.9699
