中文摘要：

讨论了基于Chebyshev节点的多元Lagrange求积公式在布朗片测度下的平均误差，得到了相应量的强渐近阶．在多元情形下，构造性地建立了平均框架下有关数值求积公式的误差分析，提出的算法更加简单适用，且具有一定的收敛速度．

英文摘要：

The average errors of multivariate tensor product quadrature formulae based on the Chebyshev nodes on the Brownian sheet measure are studied and the corresponding stronger asymptotic order is obtained. In the past, the average error analysis of multivariate quadrature formula is non-constructive. But the algorithm of this paper is constructive, which is simpler and more applicable. At the same time,this algorithm has a certain convergence rate.