基于重心型插值的应用研究任务书

 2021-10-17 06:10

1. 毕业设计（论文）的内容和要求

插值逼近问题广泛应用于科学技术和工程实践中，因此他有重要的理论意义与实际意义。

而重心拉格朗日插值相较于一般的拉格朗日插值具有计算量小，插值稳定性好。

重心有理插值在一定程度上相较于多项式插值具有更高的插值精度。

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2. 参考文献

[1] F. S. Acton, Numerical Methods That [Usually] Work, AMS, Providence, RI, 1990. [2] R. Baltensperger, Improving the accuracy of the matrix dierentiation method for arbitrary collocation points, Appl. Numer. Math., 33 (2000), pp. 143149. [3] R. Baltensperger and J.-P. Berrut, The errors in calculating the pseudospectral dierentiation matrices for ˇCebyˇsevGaussLobatto points, Comput. Math. Appl., 37 (1999), pp. 4148 [4] R. Baltensperger and J.-P. Berrut, The linear rational collocation method, J. Comput. Appl. Math., 134 (2001), pp. 243258. [5] R. Baltensperger and M. R. Trummer, Spectral dierencing with a twist, SIAM J. Sci. Comput., 24 (2003), pp. 14651487. [6] Z. Battles and L. N. Trefethen, An extension of MATLAB to continuous functions and operators, SIAM J. Sci. Comput., to appear. [7] A. Bayliss, A. Class, and B. Matkowsky, Roundo error in computing derivatives using the Chebyshev dierentiation matrix, J. Comput. Phys., 116 (1994), pp. 380383. [8] R. Bellman, B. G. Kashef, and J. Casti, Dierential quadrature: A technique for the rapid solution of nonlinear partial dierential equations, J. Comput. Phys., 10 (1972), pp. 4052. [9] J.-P. Berrut, Baryzentrische Formeln zur trigonometrischen Interpolation I, Z. Angew. Math. Phys. (ZAMP), 35 (1984), pp. 91105. [10] J.-P. Berrut, Barycentric formulae for cardinal (SINC-)interpolants, Numer. Math., 54 (1989), pp. 703718 (erratum: Numer. Math, 55 (1989), p. 747).

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