Linear Chebyshev approximation of complex-valued functions

Abstract

This paper is concerned with Chebyshev approximation by linear functions to complex-valued data. The problem is nonlinear, and we present a convergent algorithm for its solution. We also pose a related linear problem which is simple to solve, and which produces approximations which are near-best in the Chebyshev sense within a factor of 2 \sqrt 2 . Some numerical examples are provided.