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Splines and their properties and applications. A spline is a function defined piecewise by polynomials, and is typically used in interpolating problems.

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Interpolating between piecewise linear functions, with a family of smooth functions

As noted by Dejan Govc, the set $E$ should also contain those points where the right limit of $F(x)$ equals the left limit of $G(x)$, because any continuous function bounded between $F$ and $G$ will b …
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