Interpolation Formula
What is Interpolation?
Interpolation is an important statistical tool. It is the process of calculating a value between two points on the curve of a function from the given points which also lie on the same curve.
Why is Interpolation Important?
Interpolation is needed to compute the value of a function for an intermediate value of the independent function.
What are Piecewise Polynomials?
Approximated functions converted into polynomials, i.e., simpler forms, which would to make it easier to integrate and differentiate such functions to facilitate the calculations pertaining to areas under curves are called piecewise polynomials
What are the Various Methods of Interpolation?
The various methods of interpolation are,
- Linear Interpolation Formula
- Nearest Neighbor Method
- Quadratic Interpolation
- Lagrange Formula
- Newton Formula
What is the Use of Interpolation?
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 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 + a1ex + a2e2x +…..+ anenx
What is the Difference between Interpolation and Extrapolation?
Interpolation is the process of calculating a value between two points on the curve of a function from the given points which also lie on the same curve, whereas extrapolation is the way of predicting the magnitude of the reliant factor for an individual entity that is beyond the scope of the dataset.
Interpolation Formula
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.
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