Question

Is it easier to add a new data pair using divided-difference methods or the Lagrange polynomial in order to obtain a higher-degree polynomial?

Please may you answer this question in detail using your knowledge about Numerical analysis?

Thank your for your time!

Answer 1

Yes,It is easier to add a new data pair using divided difference method or the Lagrange polynomial in order to obtain a higher degree polynomial.Because,

We know the Lagrange's formula

When an additional node point(x​​​​​​n+1,y​​​​​​n+1) is added all the previous basis polynomial and their corresponding coefficients remains unchanged, we only need to obtain a new basis of polynomial of degree n+1

If all of n+1 node points are equally spaced,then divided difference method to find higher order polynomial can take simpler form.