Chebyshev-type quadrature on multidimensional domains
Chebyshev-type quadrature on multidimensional domains
复制标题
多维域上的切比雪夫型求积
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
J. Meyers
中科院分区：
文献类型：
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作者：
J. Korevaar;J. Meyers
摘要将区间和圆的等系数求积公式结合起来，得到了积域的切比雪夫型求积公式（相对于通常的面积或体积测度）。“多项式精确到p次所需的最小节点数N = N（p）的上界很容易遵循。下界是通过投影到某些较低维度的子集和其他方法获得的。对于正方形、立方体、圆柱形表面、圆盘和圆柱体，确定了N（p）的精确阶，而对于球体和球，找到了阶的上界和下界。改进了Bajnok和Rabau最近的结果，作者描述了由O（t3）个点组成的所谓球面t -设计（具有不同节点的球面的t阶Chebyshev型求积公式）.
Abstract Quadrature formulas with equal coefficients for interval and circle are combined to obtain Chebyshev-type quadrature formulas (relative to ordinary area or volume measure) for "product domains." Upper bounds for the minimal number N = N ( p ) of nodes required for polynomial exactness to degree p readily follow. Lower bounds are obtained by projecting onto certain subsets of lower dimension and other means. The precise order of N ( p ) is determined for square, cube, cylindrical surface, disc, and cylinder, while upper and lower bounds for the order are found for sphere and ball. Improving recent results of Bajnok and Rabau, the authors describe so-called spherical t -designs (Chebyshev-type quadrature formulas of degree t for the sphere with distinct nodes) consisting of O ( t 3 ) points.