Questions on interpolation, the estimation of the value of a function from given input, based on the values of the function at known points. It is necessary because in science and engineering we often need to deal with discrete experimental data.
Interpolation is a useful mathematical and statistical tool used to estimate values between two points on a line or curve.
What Is Interpolation?
Interpolation is the process of deriving a simple function from a set of discrete data points so that the function passes through all the given data points (i.e. reproduces the data points exactly) and can be used to estimate data points in-between the given ones.
To help us remember what it means, we should think of the first part of the word, 'inter,' as meaning 'enter,' which reminds us to look 'inside' the data we originally had.
Applications: This tool, interpolation, is not only useful in statistics, but is also useful in science, business or any time there is a need to predict values that fall within two existing data points. It is also used to simplify complicated functions by sampling data points and interpolating them using a simpler function. In the mathematical field of numerical analysis, interpolation is a method of constructing new data points within the range of a discrete set of known data points. In engineering and science, one often has a number of data points, obtained by sampling or experimentation, which represent the values of a function for a limited number of values of the independent variable. It is often required to interpolate, i.e., estimate the value of that function for an intermediate value of the independent variable.
The details, techniques, and precise meaning of interpolation depend heavily on the sub-discipline of mathematics, therefore you are encouraged to use additional subject tags such as regression, operator-theory, interpolation-theory, or signal-processing when appropriate.