Why the plots of spline and cubic interpolation are exactly same? [closed]

1. Is spline interpolation cubic?
2. Why is cubic spline interpolation better?
3. What is a natural cubic spline how is it different from the cubic spline?
4. What is an advantage of cubic spline interpolation compared to Lagrange interpolation?

Is spline interpolation cubic?

Cubic spline interpolation is a way of finding a curve that connects data points with a degree of three or less. Splines are polynomial that are smooth and continuous across a given plot and also continuous first and second derivatives where they join.

Why is cubic spline interpolation better?

Cubic spline is used as the method of interpolation because of the advantages it provides in terms of simplicity of calculation, numerical stability and smoothness of the interpolated curve.

What is a natural cubic spline how is it different from the cubic spline?

A cubic spline will have K + 3 + 1 degrees of freedom. A natural spline has K + 3 + 1 - 5 degrees of freedom due to the constraints at the endpoints. A further constraint can be added to reduce overfitting by enforcing smoothness in the spline.

What is an advantage of cubic spline interpolation compared to Lagrange interpolation?

Cubic spline interpolation is a special case for Spline interpolation that is used very often to avoid the problem of Runge's phenomenon. This method gives an interpolating polynomial that is smoother and has smaller error than some other interpolating polynomials such as Lagrange polynomial and Newton polynomial.