Uses of Interpolation

Various uses of Interpolation are given below,

Deriving a Function From a Data Set

The diverse and scattered data points can be turned into a compact function using interpolation so that each point in the data travels through the curve of such a function. This makes it so much easier to understand the whole data in just one glance. Data can be converted into the following form:

p(x) = a₀ + a₁e^x + a₂e^2x +…..+ a_ne^nx

Obtaining Piecewise Polynomials

With the help of interpolation, one can also approximate functions into polynomials, i.e., simpler forms, which would make it easier to integrate and differentiate such functions to facilitate the calculations pertaining to areas under curves.

Many a time, the problems involving integration are very difficult to be solved analytically. In such cases, interpolation is used to alter the integrands and polynomials to make calculations easier.

Interpolation formula is a method to find new values of any function using the set of available values through interpolation. It is an important statistical tool used to calculate the value between two points on the curve of a function from the given points which also lie on the same curve.

In statistical analysis and interpretation, sometimes it is found that a given series happens to be incomplete rather than complete, i.e., some values in the series remain unknown. But to derive correct results, it becomes essential to find the missing or unknown values in the series. The statistical technique that is used to estimate the unknown values on the basis of available data is called interpolation.