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Homogeneous Splines

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spline degree
1
2
3
4
derivative degree
0
1
2
3
4
interpolating polynomial
A polynomial spline of homogeneous degree
n
(or simply a homogeneous spline) is a piecewise polynomial,
(n-1)
-times continuously differentiable function interpolating a list of points (knots) in the plane. If the points are equally spaced, the spline is said to be uniform, and otherwise nonuniform. Importantly, homogeneous (nonuniform) splines may be used in lieu of the usual Lagrange interpolating polynomials, because they mitigate the oscillation problems due to (general) Runge's phenomenon.
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