A fundamental problem encountered quite often in
mathematics,
econometrics and other disciplines is that of
curve fitting.
Curve fitting - regardless of the specific
algorithim used - is most easily thought of as a process of
filling in the blanks.
In other words, we have a
series of data points. These points are generated by a mathematical process, the
details of which are precisely unknown to us. We wish to calculate the value of other,
intermediate points which lie between any two known points. The value of these intermediate data points is
unknown.
Linear Interpolation, then, is simply an algorithim which allows the user to calculate what essentially is an
average value. Note that this process of averaging makes an
implicit assumption that the underlying process generating data moves
rather slowly; in other words, we would not expect much activity in
second or
higher order derivatives.
There are many other algorithims commonly used to solve this problem, for example,
cubic splines or
exponential fitting.