【摘 要】
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The purpose of this paper is to study the maximum trigonometric de-gree of the quadrature formula associated with m prescribed nodes and n unknown additional no
【机 构】
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School of Mathematical Sciences
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The purpose of this paper is to study the maximum trigonometric de-gree of the quadrature formula associated with m prescribed nodes and n unknown additional nodes in the interval (-π,π]. We show that for a fixed n, the quadrature formulae with m and m+1 prescribed nodes share the same maximum degree if m is odd. We also give necessary and sufficient conditions for all the additional nodes to be real, pairwise distinct and in the interval (-π,π] for even m, which can be obtained constructively. Some numerical examples are given by choosing the prescribed nodes to be the zeros of Chebyshev polynomials of the second kind or randomly for m≥3.
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