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//Example 5.29
//Divided Difference Interpolation
//Page no. 167
clc;close;clear;
x=[4,5,7,10,11,13]
y=[48,100,294,900,1210,2028];
y1=y;
deff('yi=P(a,b,d,e)','yi=(b(d+1)-b(d))/(a(d+e)-a(d))') //function for finding polynomials
for i=1:6
for j=1:6-i
z(j,i)=P(x,y,j,i)
y(j)=z(j,i)
end
end
z(6,1)=0;
printf('x\ty f(x0,x1) f(x0,x1,x3) f(x0,x1,x2,x3) f(x0,x1,x2,x3,x4)\n')
printf('---------------------------------------------------------------------------------\n')
for j=1:5
printf(' %i\t%i \t%i\t\t%i\t\t%i\t\t %i %i\n',x(1,j),y1(1,j),z(j,1),z(j,2),z(j,3),z(j,4),z(j,5))
end
deff('y=f(x1)','y=y1(1)+(x1-x(1))*z(1,1)+(x1-x(1))*(x1-x(2))*z(1,2)+(x1-x(1))*(x1-x(2))*(x1-x(3))*z(1,3)')
printf('\n\nf(8) = %g',f(8))
printf('\n\nf(15) = %i',f(15))
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