TRIGONOMETRIC GENERATING FUNCTION METHODS AND THE SIGN FUNCTION

Abstract

The sign function f(x) = sgn(x) has many applications. It's approximations bypolynomials and rational functions have been studied by several authors. Truncated Fourierseries and trigonometric interpolants converge slowly for functions with jumps in value, thenonlinear Fourier approximants with better convergence based on trigonometric generatingfunctions are developed. The convergence and error terms are obtained.