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interpolation.

ESAIM: Control, Optimisation and Calculus of Variations (1)

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Statistical Estimates for Generalized Splines
Magnus Egerstedt, Clyde Martin
Journal:

ESAIM: Control, Optimisation and Calculus of Variations / Volume 9 / January 2003

Published online by Cambridge University Press:

15 September 2003, pp. 553-562

Print publication:

January 2003
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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.