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.
Highlights
International Journal of Submit your manuscripts at http://www.hindawi.com
International Journal of Mathematics and Mathematical Sciences
Summary
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.