Sensitivity analysis for Szegő polynomials

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Szegő polynomials are orthogonal with respect to an inner product on the unit circle. Numerical methods for weighted least-squares approximation by trigonometric polynomials conveniently can be derived and expressed with the aid of Szegő polynomials. This paper discusses the conditioning of several mappings involving Szegő polynomials and, thereby, sheds light on the sensitivity of some approximation problems involving trigonometric polynomials.