Positive trigonometric quadrature formulas and quadrature on the unit circle
نویسنده
چکیده
We give several descriptions of positive quadrature formulas which are exact for trigonometric-, respectively, Laurent polynomials of degree less or equal to n − 1 − m, 0 ≤ m ≤ n − 1. 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 paraorthogonal polynomials are obtained. Finally, asymptotics for the quadrature weights are presented.
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ورودعنوان ژورنال:
- Math. Comput.
دوره 80 شماره
صفحات -
تاریخ انتشار 2011