Question

Newton's Forward Interpolation Formula is applicable when the interpolating point lies_______​

Answer 1

Step-by-step explanation:

Newton's Interpolation Formulae

As stated earlier, interpolation is the process of approximating a given function, whose values are known at $ N+1$ tabular points, by a suitable polynomial, $ P_N(x),$ of degree $ N$ which takes the values $ y_i$ at $ x=x_i$ for $ i=0,1,\ldots,N.$ Note that if the given data has errors, it will also be reflected in the polynomial so obtained.

In the following, we shall use forward and backward differences to obtain polynomial function approximating $ y = f(x),$ when the tabular points $ x_i$ 's are equally spaced. Let

$\displaystyle f(x) \approx P_N(x),$

where the polynomial $ P_N(x)$ is given in the following form: