Polynomial interpolation is a method of estimation, used when the data is thought to be generated by a polynomial function. The function is then approximated by a polynomial of a lower degree, by fitting the polynomial to the data. This process is known as polynomial fitting.

##### Where is polynomial interpolation used?

Polynomial interpolation is used in many fields of mathematics, computer science, and engineering. It is a method of approximating a function by a polynomial. There are many different ways to interpolate a function, and the choice of interpolation method depends on the application. Some common methods of interpolation include Lagrange interpolation, Newton interpolation, and Hermite interpolation.

Polynomial interpolation is used in numerical analysis to approximate functions. It is also used in computer graphics to generate smoother curves. In engineering, polynomial interpolation is used to approximate transfer functions. Why is interpolation a polynomial? Interpolation is a polynomial because it is a mathematical function that allows for the estimation of values between known data points. What is the difference between linear interpolation and polynomial interpolation? Linear interpolation is a method of estimating values between two known points by drawing a line between those points. Polynomial interpolation is a method of estimating values between two known points by fitting a polynomial to those points.

##### Why interpolation methods are used?

Interpolation methods are used in order to estimate the value of a function at a point that lies between two known data points. This is done by constructing a function that passes through the two known data points and then using this function to estimate the value of the function at the desired point. There are many different interpolation methods that can be used, and the choice of which one to use will depend on the specific problem that you are trying to solve.

### What are the limitations of polynomial interpolation?

The limitations of polynomial interpolation are that it can only be used on data that is well-behaved (i.e. smooth and continuous), and it is not very accurate when extrapolating beyond the range of data points used to generate the interpolating polynomial. Additionally, polynomial interpolation can be sensitive to outliers in the data set.