Definition
A spline is a piecewise-polynomial real function
on an interval composed of k ordered disjoint subintervals with
- .
The restriction of S to an interval i is a polynomial
- ,
so that
The highest order of the polynomials is said to be the order of the spline S. If all subintervals are of the same length, the spline is said to be uniform and non-uniform otherwise.
The idea is to choose the polynomials in a way that guarantees sufficient smoothness of S. Specifically, for a spline of order n, S is required to be continuously differentiable to order n-1 at the interior points : for all and all ,
.
Read more about this topic: Spline (mathematics)
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