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Positive trigonometric Quadrature Formulas and quadrature on the unit circle
We give several descriptions of positive quadrature formulas which are exact
for trigonometric -, respectively, Laurent polynomials of degree less or equal
, . A complete and simple description is obtained with
the help of orthogonal polynomials on the unit circle. In particular it is
shown that the nodes polynomial can be generated by a simple recurrence
relation. As a byproduct interlacing properties of zeros of para-orthogonal
polynomials are obtained. Finally, asymptotics for the quadrature weights are
presented.Comment: Submitted by F. Peherstorfer to Math. Com