摘要
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 n3/4 ＋ O（n^2） nodes of a cubature formula on [-1,1]^3.
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+(?)(n^2) nodes of a cubature formula on [-1,1]~3.
基金
supported by NSFC Grants 10601056,10431050 and 60573023
supported by National Basic Research Program grant 2005CB321702
supported by NSF Grant DMS-0604056.
