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2004 Control Theoretic Smoothing Splines are Approximate Linear Filters
W. Dayawansa, C. Martin, Y. Zhou
Commun. Inf. Syst. 4(3): 253-272 (2004).

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.

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W. Dayawansa. C. Martin. Y. Zhou. "Control Theoretic Smoothing Splines are Approximate Linear Filters." Commun. Inf. Syst. 4 (3) 253 - 272, 2004.

Information

Published: 2004
First available in Project Euclid: 30 September 2005

zbMATH: 1090.41003
MathSciNet: MR2200878

Rights: Copyright © 2004 International Press of Boston

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Vol.4 • No. 3 • 2004
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