Definition:Spline Function/Knot
< Definition:Spline Function(Redirected from Definition:Node 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 $T$.
The points $T := \set {t_0, t_1, t_2, \ldots, t_{n - 1}, t_n}$ of $S$ are known as the knots.
Knot Vector
The ordered $n + 1$-tuple $\mathbf t := \tuple {t_0, t_1, t_2, \ldots, t_{n - 1}, t_n}$ of $S$ is known as the knot vector.
Also known as
The knots of a spline function are also known as nodes.
Some sources refer to them as control points.
Also see
- Results about knots of splines can be found here.
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): spline-fitting
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): approximation theory
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): approximation theory