报告题目：A Random Integration Algorithm for High-dimensional Function Spaces

报 告 人：张海樟 教授（中山大学）

报告时间：2026年07月13日（星期一）10:00—11:30

报告地点：数学科学学院创客基地楼111A

校内联系人：徐敏 副教授         联系方式：84708351-8208

报告摘要：We introduce a novel random integration algorithm that exhibits a high convergence order for functions characterized by sparse frequencies or rapidly decaying Fourier coefficients. Specifically, for integration in periodic isotropic Sobolev spaces and isotropic Sobolev spaces with compact support, our approach achieves a nearly optimal root mean square error (RMSE) bound.  In contrast to previous nearly optimal algorithms, our method exhibits polynomial tractability. Our integration algorithm also enjoys nearly optimal bound for weighted Sobolev space. By incorporating the trick of change of variable, our algorithm is proven to achieve the semi-exponential convergence order for the integration of analytic functions, which marks a significant improvement over the previously obtained super-polynomial convergence order. Furthermore, for integration involving Wiener-type functions, the sample complexity of our algorithm remains independent of the decay rate of the Fourier coefficients. This is a joint work with Liang Chen and Minqiang Xu.

报告人简介：张海樟，现任中山大学数学教授，中山大学逸仙学者。研究兴趣包括学习理论、应用调和分析和函数逼近. 代表性成果有再生核的Weierstrass逼近定理, 深度神经网络的收敛性理论，以及再生核巴拿赫空间理论. 在Journal of Machine Learning Research、Applied and Computational Harmonic Analysis、Mathematics of Computation、 Neural Networks、Constructive Approximation、IEEE Transactions系列等发表多篇原创性工作, 单篇最高他引超过400次. 主持包括优秀青年基金在内的多项国家和省部级基金.