Communications in Information & Systems

Control Theoretic Smoothing Splines are Approximate Linear Filters

W. Dayawansa, C. Martin, and Y. Zhou

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Abstract

The problem of constructing and approximating control theoretic smoothing splines is considered in this paper. It is shown that the optimal approximating function can be given as the solution of a forced Hamiltonian system, that can be explicitly solved using the Riccati transform, and an explicit linear filter can be constructed. We show that the bandwidth of the filter can be naturally controlled and thus for control theoretic smoothing splines the far past and the far future are unimportant. Hence smoothing splines are “local” in nature rather than "global". We conclude that while spline approximations are not causal the far future is not important.

Article information

Source
Commun. Inf. Syst., Volume 4, Number 3 (2004), 253-272.

Dates
First available in Project Euclid: 30 September 2005

Permanent link to this document
https://projecteuclid.org/euclid.cis/1128087067

Mathematical Reviews number (MathSciNet)
MR2200878

Zentralblatt MATH identifier
1090.41003

Citation

Zhou, Y.; Dayawansa, W.; Martin, C. Control Theoretic Smoothing Splines are Approximate Linear Filters. Commun. Inf. Syst. 4 (2004), no. 3, 253--272. https://projecteuclid.org/euclid.cis/1128087067


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