Fitting piecewise splines to noisy data

1. What is the purpose of smoothing spline?
2. How are splines fit?

What is the purpose of smoothing spline?

means we obtain a smoother curve by getting farther from the given data.

How are splines fit?

Basic Concepts. Spline fitting or spline interpolation is a way to draw a smooth curve through n+1 points (x₀, y₀), …, (x_n,y_n). Thus, we seek a smooth function f(x) so that f(x_i) = y_i for all i. In particular, we seek n cubic polynomials p₀, …, p_n-1 so that f(x) = p_i(x) for all x in the interval [x_i, x_i+1].