Polynomial interpolation is a mathematical method used to find a polynomial function that passes through a given set of points. It works by using a set of data points to construct a polynomial function that can accurately represent the data.
Polynomial interpolation has various applications in fields such as engineering, physics, economics, and computer graphics. It is used to approximate data points, interpolate missing data, and create smooth curves.
Polynomial interpolation is used to find a polynomial function that passes through a given set of points, while polynomial regression is used to find the best-fit polynomial curve for a given set of data points.
One limitation of polynomial interpolation is that it can only be used on a small set of data points. As the degree of the polynomial increases, it can lead to overfitting and inaccurate results. Additionally, it may not accurately represent non-polynomial data.
The degree of the polynomial in polynomial interpolation is chosen based on the number of data points and the complexity of the data. A higher degree polynomial may fit the data better, but it can also lead to overfitting. It is important to balance accuracy and simplicity when choosing the degree of the polynomial.