The Approximation of Hermite Interpolation on the Weighted Mean Norm

Xin Wang; Chong Hu; Xiuxiu Ma

doi:10.4236/ajcm.2015.53033

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American Journal of Computational Mathem... > Vol.5 No.3, September 2015

The Approximation of Hermite Interpolation on the Weighted Mean Norm ()

¹Department of Mathematics and Computer, Baoding University, Baoding, China.
²Institute of Nuclear Technology, China Institute of Atomic Energy, Beijing, China.
³Institute of Mathematical, North China Electric Power University, Baoding, China.

DOI: 10.4236/ajcm.2015.53033 PDF HTML XML 4,334 Downloads 4,782 Views

Abstract

We research the simultaneous approximation problem of the higher-order Hermite interpolation based on the zeros of the second Chebyshev polynomials under weighted Lp-norm. The estimation is sharp.

Keywords

Hermite Interpolation operator，Chebyshev polynomial，derivative approximation

Share and Cite:

Wang, X. , Hu, C. and Ma, X. (2015) The Approximation of Hermite Interpolation on the Weighted Mean Norm. American Journal of Computational Mathematics, 5, 387-392. doi: 10.4236/ajcm.2015.53033.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Szabados, J. and Vestesi, P. (1992) A Survey on Mean Convergence of Interpolatory Processes. Journal of Computational and Applied Mathematics, 43, 3-18. http://dx.doi.org/10.1016/0377-0427(92)90256-W
[2]	Szabados, J. and Vertesi, P. (1990) Interpolation of Functions. World Scientific, Singapore.
[3]	Wang, X. (2011) The Approximation of Hermite Interpolation on the Weighted Mean Norm. Journal of Tianjin Normal University, 31, 7-12.
[4]	Xia, Y. and Xu, G.Q. (2010) The Approximation of Hermite Interpolation on the Weighted Mean Norm. Journal of Tianjin Normal University, 31, 6-10.
[5]	Xu, G.Q., Cui, R. and Wang, X. (2009) The Simultaneous Approximation of Quasi-Hermite Interpolation on the Weighted Mean Norm. International Journal of Wavelets, Multiresolution and Information Processing, 7, 825-837. http://dx.doi.org/10.1142/S0219691309003276
[6]	Xie, T.F. and Zhou, S.P. (1998) Real Function Approximation Theory. Hangzhou University Press, Hangzhou.
[7]	Kingore, T. (1993) An Elementary Simultaneous Polynomials. Proceedings of the American Mathematical Society, 118, 529-536. http://dx.doi.org/10.1090/S0002-9939-1993-1129881-X