Question

What i use for finding polynomial of f(x) in lagrange interpolation?

Answer 1

● The Lagrange interpolating polynomial is the polynomial P(x) of degree <=(n-1) that passes through the n points (x_1,y_1=f(x_1)), (x_2,y_2=f(x_2)), ..., (x_n,y_n=f(x_n)), and is given by

P(x)=sum_(j=1)^nP_j(x),

(1)

where

P_j(x)=y_jproduct_(k=1; k!=j)^n(x-x_k)/(x_j-x_k).

(2)

Written explicitly,

P(x) = ((x-x_2)(x-x_3)...(x-x_n))/((x_1-x_2)(x_1-x_3)...(x_1-x_n))y_1+((x-x_1)(x-x_3)...(x-x_n))/((x_2-x_1)(x_2-x_3)...(x_2-x_n))y_2+...+((x-x_1)(x-x_2)...(x-x_(n-1)))/((x_n-x_1)(x_n-x_2)...(x_n-x_(n-1)))y_n.