It may also be appropriate to determine Szegő polynomials in algorithms for least-squares approximation of real-valued periodic functions by trigonometric polynomials.
Many algorithms for polynomial least-squares approximation of a real-valuedfunction on a real interval determine polynomials that are orthogonal with respect to a suitable inner product defined on this interval.
Analogously, it is convenient to compute Szegő polynomials, i.e., polynomials that are orthogonal with respect to an inner product on the unit circle, when approximating a complex-valued function on the unit circle in the least-squares sense.
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We describe a data-fitting application that illustrates how our scheme can be combined with the fast-Fourier-transform algorithm when the given nodes are not equidistant.