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Approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby.

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Interpolation splines of bounded curvature

Given $n$ points $p_i=(x_i,y_i)$ on the [Euclidean] plane, and a positive real number $\rho$. Can we have a polynomial spline (e.g., natural cubic spline) passing through all these points, such that: …