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Volume 2, Issue 2
Cubature Formula and Interpolation on the Cubic Domain

Huiyuan Li, Jiachang Sun & Yuan Xu

Numer. Math. Theor. Meth. Appl., 2 (2009), pp. 119-152.

Published online: 2009-02

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  • Abstract

Several cubature formulas on the cubic domains are derived using the discrete Fourier analysis associated with lattice tiling, as developed in [10]. The main results consist of a new derivation of the Gaussian type cubature for the product Chebyshev weight functions and associated interpolation polynomials on $[-1,1]^2$, as well as new results on $[-1,1]^3$. In particular, compact formulas for the fundamental interpolation polynomials are derived, based on $n^3/4 +O(n^2)$ nodes of a cubature formula on $[-1,1]^3$.

  • Keywords

Lattice, cubature, interpolation, discrete Fourier series.

  • AMS Subject Headings

41A05, 41A10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-2-119, author = {Huiyuan Li, Jiachang Sun and Yuan Xu}, title = {Cubature Formula and Interpolation on the Cubic Domain}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2009}, volume = {2}, number = {2}, pages = {119--152}, abstract = {

Several cubature formulas on the cubic domains are derived using the discrete Fourier analysis associated with lattice tiling, as developed in [10]. The main results consist of a new derivation of the Gaussian type cubature for the product Chebyshev weight functions and associated interpolation polynomials on $[-1,1]^2$, as well as new results on $[-1,1]^3$. In particular, compact formulas for the fundamental interpolation polynomials are derived, based on $n^3/4 +O(n^2)$ nodes of a cubature formula on $[-1,1]^3$.

}, issn = {2079-7338}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/nmtma/6019.html} }
TY - JOUR T1 - Cubature Formula and Interpolation on the Cubic Domain AU - Huiyuan Li, Jiachang Sun & Yuan Xu JO - Numerical Mathematics: Theory, Methods and Applications VL - 2 SP - 119 EP - 152 PY - 2009 DA - 2009/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/nmtma/6019.html KW - Lattice, cubature, interpolation, discrete Fourier series. AB -

Several cubature formulas on the cubic domains are derived using the discrete Fourier analysis associated with lattice tiling, as developed in [10]. The main results consist of a new derivation of the Gaussian type cubature for the product Chebyshev weight functions and associated interpolation polynomials on $[-1,1]^2$, as well as new results on $[-1,1]^3$. In particular, compact formulas for the fundamental interpolation polynomials are derived, based on $n^3/4 +O(n^2)$ nodes of a cubature formula on $[-1,1]^3$.

Huiyuan Li, Jiachang Sun and Yuan Xu. (2009). Cubature Formula and Interpolation on the Cubic Domain. Numerical Mathematics: Theory, Methods and Applications. 2 (2). 119-152. doi:
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