Year: 2009
Numerical Mathematics: Theory, Methods and Applications, Vol. 2 (2009), Iss. 2 : pp. 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 $[-1,1]^3$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2009-NMTMA-6019
Numerical Mathematics: Theory, Methods and Applications, Vol. 2 (2009), Iss. 2 : pp. 119–152
Published online: 2009-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 34
Keywords: Lattice cubature interpolation discrete Fourier series.