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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.

2 votes

Spline fit with bounded derivations

See section 6.5.2 of the book "Convex Optimization" by Stephen Boyd and Lieven Vandenberghe. It's available on the web as a pdf file or as a quite reasonably priced printed book from Cambridge Univer …
Brian Borchers's user avatar
5 votes

Approximating derivatives between gridpoints

Lagrange interpolation is the classic approach to this problem. In order for it to work, you'll need very precise function values, since the problem of numerical differentiation is ill-conditioned. …
Brian Borchers's user avatar