Displaying similar documents to “The Derivation of Cubic Splines with Obstacles by Methods of Optimization and Optimal Control.”

Quartic X-Splines.

R. Smarzewski, A. Bujalska-Horbowicz (1984)

Numerische Mathematik

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Statistical estimates for generalized splines

Magnus Egerstedt, Clyde Martin (2003)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper it is shown that the generalized smoothing spline obtained by solving an optimal control problem for a linear control system converges to a deterministic curve even when the data points are perturbed by random noise. We furthermore show that such a spline acts as a filter for white noise. Examples are constructed that support the practical usefulness of the method as well as gives some hints as to the speed of convergence.