Higher order spline interpolation

1. What is order in spline interpolation?
2. Can splines be used for interpolation?
3. What is Pchip interpolation?
4. Why is cubic spline interpolation better?

What is order in spline interpolation?

The "order" of the spline is the order of these "piecewise" polynomials. Source: Google. As you can see, a linear spline (order=1) fits degree one polynomials (straight ines) between the ranges, while a 7th order Spline fits 7th order polynomials.

Can splines be used for interpolation?

The Spline tool uses an interpolation method that estimates values using a mathematical function that minimizes overall surface curvature, resulting in a smooth surface that passes exactly through the input points.

What is Pchip interpolation?

pchip interpolates using a piecewise cubic polynomial P ( x ) with these properties: On each subinterval x k ≤ x ≤ x k + 1 , the polynomial P ( x ) is a cubic Hermite interpolating polynomial for the given data points with specified derivatives (slopes) at the interpolation points.

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.