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SUN Xue-nan1, HE Jia-xing1, CUI Mao-yuan2
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Abstract: The present paper introduces a combinatorial trigonomet ric polynomial operator Sn(f;r,θ) (where r is a given natural number) based on the values of f(θ) (where f(θ)∈C2π〖KG*2〗and f(θ ) is an odd function) with the nodes θk=kπ/(n+1)n k=1. It has been proved that Sn(f;r,θ) uniformly converges to f(θ) (f(θ)∈C2π and f(θ) is an odd function) on the total real axis. And Sn(f;r,θ) reaches the best approximation order when used to approxim ate to f(θ) where f(θ)∈Cj2π (0≤j≤r-1) and f(θ) is an odd function.
Key words: combinatorial trigonometric interpolation polynomial, u niform convergence, best convergence order
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SUN Xue-nan, HE Jia-xing, CUI Mao-yuan. Combinatorial trigonometric interpolation polynomial[J].J4, 2004, 42(01): 22-26.
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URL: http://xuebao.jlu.edu.cn/lxb/EN/
http://xuebao.jlu.edu.cn/lxb/EN/Y2004/V42/I01/22
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