I am working in a script for solve lagrange interpolation in matlab. I am new in it and i don't know how it works.
The data for interpolation are the next
X = [0 1 2 4 8]
Y = [1 5 10 24 50]
Then i build the polynomial od lagrange at this way:
syms x
l1 = ( (x-X(2)) * (x-X(3)) * (x-X(4)) * (x-X(5)) ) / ( (X(1)-X(2)) * (X(1)-X(3)) * (X(1)-X(4)) *(X(1)-X(5)) )
l2 = ( (x-X(1)) * (x-X(3)) * (x-X(4)) * (x-X(5)) ) / ( (X(2)-X(1)) * (X(2)-X(3)) * (X(2)-X(4)) *(X(2)-X(5)) )
l3 = ( (x-X(1)) * (x-X(2)) * (x-X(4)) * (x-X(5)) ) / ( (X(3)-X(1)) * (X(3)-X(2)) * (X(3)-X(4)) *(X(3)-X(5)) )
l4 = ( (x-X(1)) * (x-X(2)) * (x-X(3)) * (x-X(5)) ) / ( (X(4)-X(1)) * (X(4)-X(2)) * (X(4)-X(3)) *(X(4)-X(5)) )
l5 = ( (x-X(1)) * (x-X(2)) * (x-X(3)) * (x-X(4)) ) / ( (X(5)-X(1)) * (X(5)-X(2)) * (X(5)-X(3)) *(X(5)-X(4)) )
interp = l1*Y(1) + l2*Y(2) + l3*Y(3) + l4*Y(4) + l5*Y(5)
but then when i want evaluate it or i want plot it i don't know which is the way.
Can someone help me?
Make a symfun of it:
f(x)= l1*Y(1) + l2*Y(2) + l3*Y(3) + l4*Y(4) + l5*Y(5);
Plot it:
ezplot(f)
evaluate it:
f(1)
To increase readability, use:
f(x)=simplify(l1*Y(1) + l2*Y(2) + l3*Y(3) + l4*Y(4) + l5*Y(5))