Definition

Let $\sigma_{n}^{}$ be a subdivision of a real interval [a, b] :

a = x₀,    x₁,    ...,    x_n = b

s is a spline function of degree l, if s is an application from [a, b] in $\mathbb {R}$ such that :

• s has continuous derivatives up to the order l - 1,
• on each interval of the subdivision, s is a polynomial of degree less or equal than l.