An exchange algorithm for laurent polynomial chebyshev approximation on the unit circle

Abstract

An exchange algorithmi for weighted Laurent polynomial Chebyshev approximation of continuous functions on the unit circle in the complex plane is presented The algorithm is at least linearly convergent. The weighted real and imaginary parts are approximated separately by weighted trigonometric polynomials using the real Reinez algorithm and a near-best Laurent Polynomial approximation is obtained. Also weighted polynomial approximation of functions analytic in the open and continuous in the closed disc is treated and comparisons CF approximation are made.