基于第二类Chebyshev节点组的多元求积公式在布朗片测度下的平均误差

Average errors of multivariate quadrature formula based on the second Chebyshev nodes on the Brownian sheet measure

在布朗片测度下研究基于扩展的第二类Chebyshev节点组的多元张量积数值求积公式的平均误差问题,得到了相应量的强渐近阶.本研究算法是构造性的,更加简单实用,平均误差的收敛速度为n-1,优于蒙持卡洛算法,且一元情形在阶的意义下是最优的.

The average errors of multivariate tensor product quadrature formula based on the extended second Chebyshev nodes on the Brownian sheet measure are studied, and the corresponding stronger asymptotic order is obtained. The algorithm is constructive, which is simpler and more applicable. At the same time, this algorithm is optimal in the order sense for the univariate case setting.