Time-delay polynomial networks and rates of approximation
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 consi...
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Online Access: | http://dx.doi.org/10.1155/S1024123X98000726 |
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doaj-164021a26ffc415095dc7c3471c18dd12020-11-24T21:41:25ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51471998-01-0141597210.1155/S1024123X98000726Time-delay polynomial networks and rates of approximationIrwin W. Sandberg0Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin 78712-1084, TX, USAWe 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.http://dx.doi.org/10.1155/S1024123X98000726Polynomial networks; Nonlinear networks; Time-delay networks; Rates of approximation; Nonlinear input-output maps. |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Irwin W. Sandberg |
spellingShingle |
Irwin W. Sandberg Time-delay polynomial networks and rates of approximation Mathematical Problems in Engineering Polynomial networks; Nonlinear networks; Time-delay networks; Rates of approximation; Nonlinear input-output maps. |
author_facet |
Irwin W. Sandberg |
author_sort |
Irwin W. Sandberg |
title |
Time-delay polynomial networks and rates of approximation |
title_short |
Time-delay polynomial networks and rates of approximation |
title_full |
Time-delay polynomial networks and rates of approximation |
title_fullStr |
Time-delay polynomial networks and rates of approximation |
title_full_unstemmed |
Time-delay polynomial networks and rates of approximation |
title_sort |
time-delay polynomial networks and rates of approximation |
publisher |
Hindawi Limited |
series |
Mathematical Problems in Engineering |
issn |
1024-123X 1563-5147 |
publishDate |
1998-01-01 |
description |
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. |
topic |
Polynomial networks; Nonlinear networks; Time-delay networks; Rates of approximation; Nonlinear input-output maps. |
url |
http://dx.doi.org/10.1155/S1024123X98000726 |
work_keys_str_mv |
AT irwinwsandberg timedelaypolynomialnetworksandratesofapproximation |
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