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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 …
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. …