Linear Chebyshev Complex Function Approximation

摘要

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. Numerical examples and a FORTRAN program listing are included. 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. (Author)