Definition:Spline Function/Order
< Definition:Spline Function(Redirected from Definition:Order of Spline)
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Definition
Let $\closedint a b$ be a closed real interval.
Let $T := \set {a = t_0, t_1, t_2, \ldots, t_{n - 1}, t_n = b}$ form a subdivision of $\closedint a b$.
Let $S: \closedint a b \to \R$ be a spline function on $\closedint a b$ on $T$.
Some sources, instead of referring to the degree of a spline, use the order.
Let the maximum degree of the polynomials $P_k$ fitted between $t_k$ and $t_{k + 1}$ be $n$.
The order of $S$ is then $n + 1$.