TY - JOUR
T1 - Cubature Formula and Interpolation on the Cubic Domain
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 - <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>