  In the era of big data, we first need to manage the data, which requires us
to find missing data or predict the trend, so we need operations including
interpolation and data fitting. Interpolation is a process to discover deducing
new data points in a range through known and discrete data points. When solving
scientific and engineering problems, data points are usually obtained by
sampling, experiments, and other methods. These data may represent a finite
number of numerical functions in which the values of independent variables.
According to these data, we often want to get a continuous function, i.e.,
curve; or more dense discrete equations are consistent with known data, while
this process is called fitting. This article describes why the main idea come
out logically and how to apply various method since the definitions are already
written in the textbooks. At the same time, we give examples to help introduce
the definitions or show the applications. We divide interpolation into several
parts by their methods or functions for the structure. What comes first is the
polynomial interpolation, which contains Lagrange interpolation and Newton
interpolation, which are essential but critical. Then we introduce a typical
stepwise linear interpolation - Neville's algorithm. If we are concerned about
the derivative, it comes to Hermite interpolation; if we focus on smoothness,
it comes to cubic splines and Chebyshev nodes. Finally, in the Data fitting
part, we introduce the most typical one: the Linear squares method, which needs
to be completed by normal equations.
