Spline Interpolation

In this chapter, we will discuss the topic of spline interpolation. Spline interpolation is a powerful technique used to approximate a smooth curve or surface that passes through a given set of data points. This method proves particularly useful when we have discrete data points and need to estimate the values between those points. The core idea of spline interpolation involves constructing a spline function by piecing together multiple polynomial segments. The goal is to ensure that the resulting curve is not only smooth but also continuous. Typically, these polynomial segments are chosen to be of low degree, such as cubic polynomials (polynomials of degree 3), although other degrees can be utilized depending on the specific requirements. Within this chapter, we will cover the most important spline interpolation methods. By studying these methods, you will gain insight into how to select the appropriate spline and construct the desired curve for your data. Additionally, to enhance your understanding, the chapter includes several MATLAB programs. These programs serve as practical illustrations of how to employ these techniques in various simple cases.