SAGAR SINGH - IIT DELHI
Last Activity: 14 Years ago
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:
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,