Communications in Information & Systems

Hilbert Space Methods for Control Theoretic Splines: A Unified Treatment

Y. Zhou, M. Egerstedt, and C. Martin

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In this paper we give a basic derivation of smoothing and interpolating splines and through this derivation we show that the basic spline construction can be done through elementary Hilbert space techniques. Smoothing splines are shown to naturally separate into a filtering problem on the raw data and an interpolating spline construction. Both the filtering algorithm and the interpolating spline construction can be effectively implemented. We show that a variety of spline problems can be formulated into this common construction. By this construction we are also able to generalize the construction of smoothing splines to continuous data, a spline like filtering algorithm. Through the control theoretic approach it is natural to add multiple constraints and these techniques are developed in this paper.

Article information

Commun. Inf. Syst., Volume 6, Number 1 (2006), 55-81.

First available in Project Euclid: 5 April 2007

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 41A15: Spline approximation
Secondary: 49K15: Problems involving ordinary differential equations 93C15: Systems governed by ordinary differential equations [See also 34H05]


Zhou, Y.; Egerstedt, M.; Martin, C. Hilbert Space Methods for Control Theoretic Splines: A Unified Treatment. Commun. Inf. Syst. 6 (2006), no. 1, 55--81.

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