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# how to find if we should do the sum with newton's interpolation forward or by using backward formula by seeing the sum. 10 years ago

# 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,    