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

二、报告人：张海樟 教授

三、时  间：2026年7月3日10:00-11:00

四、地  点：A4-309

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，博士，中山大学数学学院（珠海）教授、博士生导师。本科毕业于北京师范大学数学系，硕士毕业于中国科学院数学所，博士毕业于美国雪城大学数学系，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。单篇最高他引超过360次。主持包括优秀青年基金在内的多项国家和省部级基金。为中山大学逸仙学者。

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