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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
"L_{1} 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 L_{1}
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. L_{1} splines are implemented using efficient
interior-point methods for linear programs.

**Category**: Applied Math and Analysis**Duration**: 01:18:06**Date**: March 6, 2000 at 4:00 PM**Views**: 27-
**Tags:**seminar, Applied Math Seminar

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