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| Asymptotic Representation for Remainder of Quasi-Hermite-Fejer Interpolation Polynomial |
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Citation： |
Xie Tingfan.Asymptotic Representation for Remainder of Quasi-Hermite-Fejer Interpolation Polynomial[J].Chinese Annals of Mathematics B,1985,6(4):457~464 |
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Net amount： 844 |
Authors： |
Xie Tingfan; |
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| Abstract： |
Let Q_2n+1(f,x) be the quasi-Hermite-Fejer interpolation polynomial of function f(x)\in C_[-1,1] based on the zeros of the Chebyshev polynomial of the second kind U_m(x)=\frac{sin((n+1)arccosx)}{sin(arccosx)}.In this paper, the uniform asymptotic representation for the quantity |Q_2n+1(f,x)-f(x)| is given. A similar result for the Hermite-Fejer interpolation polynomial based on the zeros of the Chebyshev polynomial of tne first kind is also established. |
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