Time-delay polynomial networks and rates of approximation

Irwin W. Sandberg

Mathematical Problems in Engineering, 1998, vol. 4, 1-14

Abstract:

We consider a large family of finite memory causal time-invariant maps G from an input set S to a set of ℝ -valued functions, with the members of both sets of functions defined on the nonnegative integers, and we give an upper bound on the error in approximating a G using a two-stage structure consisting of a tapped delay line and a static polynomial network N . This upper bound depends on the degree of the multivariable polynomial that characterizes N . Also given is a lower bound on the worst-case error in approximating a G using polynomials of a fixed maximum degree. These upper and lower bounds differ only by a multiplicative constant. We also give a corresponding result for the approximation of not-necessarily-causal input–output maps with inputs and outputs that may depend on more than one variable. This result is of interest, for example, in connection with image processing.

Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:286701

DOI: 10.1155/S1024123X98000726

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