[PDF] MT31- Méthodes numériques Spline cubique aux points [-5 -

What is a cubic spline interpolation?

In cubic spline interpolation (as shown in the following figure), the interpolating function is a set of piecewise cubic functions. Specifically, we assume that the points ( x i, y i) and ( x i + 1, y i + 1) are joined by a cubic polynomial S i ( x) = a i x 3 + b i x 2 + c i x + d i that is valid for x i ? x ? x i + 1 for i = 1, …, n ? 1.

What is the formula for spline interpolation in Python?

i+2,j+3+ B i+3,3(m i+3)Q i+3,j+3 Q. Agrapart et al. 23 Cubic and bicubic spline interpolation in Python (76) Cubic B-spline functions are resumed from the equations16to19with the proper changes of variables.

Are cubic splines better than global polynomial equations?

To obtain a smoother curve, cubic splines are frequently recommended. They are generally well behaved and continuous up to the second order derivative at the data points. Even though cubic splines are less prone to oscillation or overshoot than global polynomial equations, they do not prevent it.

How do you solve a cubic spline?

Clamped spline. The first order derivative of the splines at the end points are set to known values. In traditional cubic splines equations 2 to 5 are combined and the n+1 by n+1 tridiagonal matrix is solved to yield the cubic spline equations for each segment [1,3].