Showing papers on "Function approximation published in 1982"
TL;DR: Theoretical upper and lower bounds on the accuracy of the computed Chebyshev error are derived and efforts to extend the method to functions whose domain of definition is a continuum are discussed.
Abstract: A new computational technique is described for the Chebyshev, or minimax, approximation of a given complex valued function by means of linear combinations of given complex valued basis functions. The domain of definition of all functions can be any finite set whatever. Neither the basis functions nor the function approximated need satisfy any special hypotheses beyond the requirement that they be defined on a common domain. Theoretical upper and lower bounds on the accuracy of the computed Chebyshev error are derived. These bounds permit both a priori and a posteriori error assessments. Efforts to extend the method to functions whose domain of definition is a continuum are discussed. An application is presented involving ’’re‐shading’’ a 50‐ element antenna array to minimize the effects of a 10% element failure rate, while maintaining full steering capability and mainlobe beamwidth.
70 citations
TL;DR: In this paper, the authors give a complete characterization of functions in Co(T), where T is a locally compact subset of the real line, which have a strongly unique best approximation from an n-dimensional weak Che...
Abstract: We give a complete characterization of those functions in Co(T), where T is a locally compact subset of the real line, which have a strongly unique best approximation from an n-dimensional weak Che...
21 citations
TL;DR: The Pade approximation technique for model order reduction often exhibits two inherent deficiencies, i.e. (l) the reduced model often depicts non-minimum phase difficulties and (b) it often shows poor matching in the transient zone, although the steady state values are the same as for the parent system.
5 citations