@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 = {<p style="text-align: justify;">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 $[-1,1]^3$.</p>},
issn = {2079-7338},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/nmtma/6019.html}
}