# Statistical estimates for generalized splines

Magnus Egerstedt; Clyde Martin

ESAIM: Control, Optimisation and Calculus of Variations (2003)

- Volume: 9, page 553-562
- ISSN: 1292-8119

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topEgerstedt, Magnus, and Martin, Clyde. "Statistical estimates for generalized splines." ESAIM: Control, Optimisation and Calculus of Variations 9 (2003): 553-562. <http://eudml.org/doc/245032>.

@article{Egerstedt2003,

abstract = {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.},

author = {Egerstedt, Magnus, Martin, Clyde},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {optimal control; smoothing splines; linear systems; interpolation},

language = {eng},

pages = {553-562},

publisher = {EDP-Sciences},

title = {Statistical estimates for generalized splines},

url = {http://eudml.org/doc/245032},

volume = {9},

year = {2003},

}

TY - JOUR

AU - Egerstedt, Magnus

AU - Martin, Clyde

TI - Statistical estimates for generalized splines

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2003

PB - EDP-Sciences

VL - 9

SP - 553

EP - 562

AB - 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.

LA - eng

KW - optimal control; smoothing splines; linear systems; interpolation

UR - http://eudml.org/doc/245032

ER -

## References

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- [11] S. Sun, M. Egerstedt and C. Martin, Control Theoretic Smoothing Splines. IEEE Trans. Automat. Control 45 (2000) 2271-2279. Zbl0971.49022MR1807308
- [12] G. Wahba, Spline Models for Observational Data. CBMS-NSF Regional Conference Series in Applied Mathematics. SIAM, Philadelphia (1990). Zbl0813.62001MR1045442
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- [14] Z. Zhang, J. Tomlinson and C. Martin, Splines and Linear Control Theory. Acta Math. Appl. 49 (1997) 1-34. Zbl0892.41008MR1482878

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