# Dear Sir, I would like to know how we can find if the given problem should be done with Newtons forward interpolation formula or Newtons backward interpolation formula. Please give me the method to find it. Thank you. Anitha ashok.

SAGAR SINGH - IIT DELHI
879 Points
12 years ago

Dear student,

# Newton's Interpolation Formulae

As stated earlier, interpolation is the process of approximating a given function, whose values are known at tabular points, by a suitable polynomial, of degree which takes the values at for 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 when the tabular points 's are equally spaced. Let

where the polynomial is given in the following form:

 (11.4.1)

for some constants to be determined using the fact that for

So, for substitute in (11.4.1) to get This gives us Next,

So, For or equivalently

Thus, Now, using mathematical induction, we get

Thus,

As this uses the forward differences, it is called NEWTON'S FORWARD DIFFERENCE FORMULA for interpolation, or simply, forward interpolation formula.