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John Lavery : L_1 Splines: Shape-Preserving, Multiscale, Piecewise Polynomial Geometric Modeling

We discuss a new class of cubic interpolating and approximating "L1 splines" that preserve the shape both of smooth data and of data with abrupt changes in magnitude or spacing. The coefficients of these splines are calculated by minimizing the L1 norm of the second derivatives. These splines do not require constraints, penalties, a posteriori filtering or interaction with the user. Univariate and multivariate cases are treated in one and the same framework. L1 splines are implemented using efficient interior-point methods for linear programs.

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